Type  Label  Description 
Statement 

Theorem  19.21a3con13vVD 28701* 
Virtual deduction proof of alrim3con13v 28352. The following user's
proof is completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
1:: 
 2:: 
 3:2,?: e2 28465 
 4:2,?: e2 28465 
 5:2,?: e2 28465 
 6:1,4,?: e12 28570 
 7:3,?: e2 28465 
 8:5,?: e2 28465 
 9:7,6,8,?: e222 28470 
 10:9,?: e2 28465 
 11:10:in2 
 qed:11:in1 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  exbirVD 28702 
Virtual deduction proof of exbir 1355. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:: 
 3:: 
 5:1,2,?: e12 28570 
 6:3,5,?: e32 28604 
 7:6: 
 8:7: 
 9:8,?: e1_ 28461 
 qed:9: 

(Contributed by Alan Sare, 13Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  exbiriVD 28703 
Virtual deduction proof of exbiri 605. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
h1:: 
 2:: 
 3:: 
 4:: 
 5:2,1,?: e10 28529 
 6:3,5,?: e21 28576 
 7:4,6,?: e32 28604 
 8:7: 
 9:8: 
 qed:9: 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  rspsbc2VD 28704* 
Virtual deduction proof of rspsbc2 28353. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:: 
 3:: 
 4:1,3,?: e13 28594 
 5:1,4,?: e13 28594 
 6:2,5,?: e23 28601 
 7:6: 
 8:7: 
 qed:8: 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  3impexpVD 28705 
Virtual deduction proof of 3impexp 1356. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:: 
 3:1,2,?: e10 28529 
 4:3,?: e1_ 28461 
 5:4,?: e1_ 28461 
 6:5: 
 7:: 
 8:7,?: e1_ 28461 
 9:8,?: e1_ 28461 
 10:2,9,?: e01 28525 
 11:10: 
 qed:6,11,?: e00 28614 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  3impexpbicomVD 28706 
Virtual deduction proof of 3impexpbicom 1357. The following user's proof
is completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
1:: 
 2:: 
 3:1,2,?: e10 28529 
 4:3,?: e1_ 28461 
 5:4: 
 6:: 
 7:6,?: e1_ 28461 
 8:7,2,?: e10 28529 
 9:8: 
 qed:5,9,?: e00 28614 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  3impexpbicomiVD 28707 
Virtual deduction proof of 3impexpbicomi 1358. The following user's proof
is completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcoreleleqVD 28708* 
Virtual deduction proof of sbcoreleleq 28354. The following user's proof
is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:1,?: e1_ 28461 
 3:1,?: e1_ 28461 
 4:1,?: e1_ 28461 
 5:2,3,4,?: e111 28508 
 6:1,?: e1_ 28461 
 7:5,6: e11 28522 
 qed:7: 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  hbra2VD 28709* 
Virtual deduction proof of nfra2 2599. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
1:: 
 2:: 
 3:1,2,?: e00 28614 
 4:2: 
 5:4,?: e0_ 28618 
 qed:3,5,?: e00 28614 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  tratrbVD 28710* 
Virtual deduction proof of tratrb 28355. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:1,?: e1_ 28461 
 3:1,?: e1_ 28461 
 4:1,?: e1_ 28461 
 5:: 
 6:5,?: e2 28465 
 7:5,?: e2 28465 
 8:2,7,4,?: e121 28490 
 9:2,6,8,?: e122 28487 
 10:: 
 11:6,7,10,?: e223 28469 
 12:11: 
 13:: 
 14:12,13,?: e20 28573 
 15:: 
 16:7,15,?: e23 28601 
 17:6,16,?: e23 28601 
 18:17: 
 19:: 
 20:18,19,?: e20 28573 
 21:3,?: e1_ 28461 
 22:21,9,4,?: e121 28490 
 23:22,?: e2 28465 
 24:4,23,?: e12 28570 
 25:14,20,24,?: e222 28470 
 26:25: 
 27:: 
 28:27,?: e0_ 28618 
 29:28,26: 
 30:: 
 31:30,?: e0_ 28618 
 32:31,29: 
 33:32,?: e1_ 28461 
 qed:33: 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  3ax5VD 28711 
Virtual deduction proof of 3ax5 28356. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:1,?: e1_ 28461 
 3:: 
 4:2,3,?: e10 28529 
 qed:4: 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  syl5impVD 28712 
Virtual deduction proof of syl5imp 28330. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's StepSelector
to pick all remaining steps of the Metamath proof.
1:: 
 2:1,?: e1_ 28461 
 3:: 
 4:3,2,?: e21 28576 
 5:4,?: e2 28465 
 6:5: 
 qed:6: 

(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  idiVD 28713 
Virtual deduction proof of idi 2. The following user's
proof is completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
(Contributed by Alan Sare, 31Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  ancomsimpVD 28714 
Closed form of ancoms 439. The following user's proof is completed by
invoking mmj2's unify command and using mmj2's StepSelector to pick all
remaining steps of the Metamath proof.
(Contributed by Alan Sare, 25Dec2011.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  ssralv2VD 28715* 
Quantification restricted to a subclass for two quantifiers. ssralv 3239
for two quantifiers. The following User's Proof is a Virtual Deduction
proof completed automatically by the tools program
completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. ssralv2 28350 is ssralv2VD 28715 without
virtual deductions and was automatically derived from ssralv2VD 28715.
1:: 
 2:: 
 3:1: 
 4:3,2: 
 5:4: 
 6:5: 
 7:: 
 8:7,6: 
 9:1: 
 10:9,8: 
 11:10: 
 12:: 
 13:: 
 14:12,13,11: 
 15:14: 
 16:15: 
 qed:16: 

(Contributed by Alan Sare, 10Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  ordelordALTVD 28716 
An element of an ordinal class is ordinal. Proposition 7.6 of
[TakeutiZaring] p. 36. This is an alternate proof of ordelord 4416 using
the Axiom of Regularity indirectly through dford2 7323. dford2 is a
weaker definition of ordinal number. Given the Axiom of Regularity, it
need not be assumed that because this is inferred by the
Axiom of Regularity. The following User's Proof is a Virtual Deduction
proof completed automatically by the tools program
completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. ordelordALT 28357 is ordelordALTVD 28716
without virtual deductions and was automatically derived from
ordelordALTVD 28716 using the tools program
translate..without..overwriting.cmd and Metamath's minimize command.
1:: 
 2:1: 
 3:1: 
 4:2: 
 5:2: 
 6:4,3: 
 7:6,6,5: 
 8:: 
 9:8: 
 10:9: 
 11:10: 
 12:11: 
 13:12: 
 14:13: 
 15:14,5: 
 16:4,15,3: 
 17:16,7: 
 qed:17: 

(Contributed by Alan Sare, 12Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  equncomVD 28717 
If a class equals the union of two other classes, then it equals the
union of those two classes commuted. The following User's Proof is a
Virtual Deduction proof completed automatically by the tools program
completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. equncom 3322 is equncomVD 28717 without
virtual deductions and was automatically derived from equncomVD 28717.
1:: 
 2:: 
 3:1,2: 
 4:3: 
 5:: 
 6:5,2: 
 7:6: 
 8:4,7: 

(Contributed by Alan Sare, 17Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  equncomiVD 28718 
Inference form of equncom 3322. The following User's Proof is a
Virtual Deduction proof completed automatically by the tools program
completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. equncomi 3323 is equncomiVD 28718 without
virtual deductions and was automatically derived from equncomiVD 28718.
(Contributed by Alan Sare, 18Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sucidALTVD 28719 
A set belongs to its successor. Alternate proof of sucid 4473.
The following User's Proof is a Virtual Deduction proof
completed automatically by the tools program
completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. sucidALT 28720 is sucidALTVD 28719
without virtual deductions and was automatically derived from
sucidALTVD 28719. This proof illustrates that
completeusersproof.cmd will generate a Metamath proof from any
User's Proof which is "conventional" in the sense that no step
is a virtual deduction, provided that all necessary unification
theorems and transformation deductions are in set.mm.
completeusersproof.cmd automatically converts such a
conventional proof into a Virtual Deduction proof for which each
step happens to be a 0virtual hypothesis virtual deduction.
The user does not need to search for reference theorem labels or
deduction labels nor does he(she) need to use theorems and
deductions which unify with reference theorems and deductions in
set.mm. All that is necessary is that each theorem or deduction
of the User's Proof unifies with some reference theorem or
deduction in set.mm or is a semantic variation of some theorem
or deduction which unifies with some reference theorem or
deduction in set.mm. The definition of "semantic variation" has
not been precisely defined. If it is obvious that a theorem or
deduction has the same meaning as another theorem or deduction,
then it is a semantic variation of the latter theorem or
deduction. For example, step 4 of the User's Proof is a
semantic variation of the definition (axiom)
, which unifies with dfsuc 4400, a
reference definition (axiom) in set.mm. Also, a theorem or
deduction is said to be a semantic variation of another
theorem or deduction if it is obvious upon cursory inspection
that it has the same meaning as a weaker form of the latter
theorem or deduction. For example, the deduction
infers is a
semantic variation of the theorem
, which unifies with
the set.mm reference definition (axiom) dford2 7323.
h1:: 
 2:1: 
 3:2: 
 4:: 
 qed:3,4: 

(Contributed by Alan Sare, 18Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sucidALT 28720 
A set belongs to its successor. This proof was automatically derived
from sucidALTVD 28719 using translate_{without}_overwriting.cmd and
minimizing. (Contributed by Alan Sare, 18Feb2012.)
(Proof modification is discouraged.) (New usage is discouraged.)



Theorem  sucidVD 28721 
A set belongs to its successor. The following User's Proof is a
Virtual Deduction proof completed automatically by the tools
program completeusersproof.cmd, which invokes Mel O'Cat's mmj2
and Norm Megill's Metamath Proof Assistant. sucid 4473 is
sucidVD 28721 without virtual deductions and was automatically
derived from sucidVD 28721.
h1:: 
 2:1: 
 3:2: 
 4:: 
 qed:3,4: 

(Contributed by Alan Sare, 18Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  imbi12VD 28722 
Implication form of imbi12i 316. The following User's Proof is a Virtual
Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. imbi12 28338
is imbi12VD 28722 without virtual deductions and was automatically derived
from imbi12VD 28722.
1:: 
 2:: 
 3:: 
 4:1,3: 
 5:2,4: 
 6:5: 
 7:: 
 8:1,7: 
 9:2,8: 
 10:9: 
 11:6,10: 
 12:11: 
 qed:12: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  imbi13VD 28723 
Join three logical equivalences to form equivalence of implications. The
following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. imbi13 28339
is imbi13VD 28723 without virtual deductions and was automatically derived
from imbi13VD 28723.
1:: 
 2:: 
 3:: 
 4:2,3: 
 5:1,4: 
 6:5: 
 7:6: 
 qed:7: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcim2gVD 28724 
Distribution of class substitution over a leftnested implication.
Similar
to sbcimg 3034. The following User's Proof is a Virtual Deduction proof
completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. sbcim2g 28358
is sbcim2gVD 28724 without virtual deductions and was automatically derived
from sbcim2gVD 28724.
1:: 
 2:: 
 3:1,2: 
 4:1: 
 5:3,4: 
 6:5: 
 7:: 
 8:4,7: 
 9:1: 
 10:8,9: 
 11:10: 
 12:6,11: 
 qed:12: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcbiVD 28725 
Implication form of sbcbiiOLD 3049. The following User's Proof is a
Virtual
Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. sbcbi 28359
is sbcbiVD 28725 without virtual deductions and was automatically derived
from sbcbiVD 28725.
1:: 
 2:: 
 3:1,2: 
 4:1,3: 
 5:4: 
 qed:5: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  trsbcVD 28726* 
Formulabuilding inference rule for class substitution, substituting a
class
variable for the set variable of the transitivity predicate. The
following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. trsbc 28360
is trsbcVD 28726 without virtual deductions and was automatically derived
from trsbcVD 28726.
1:: 
 2:1: 
 3:1: 
 4:1: 
 5:1,2,3,4: 
 6:1: 
 7:5,6: 
 8:: 
 9:7,8: 
 10:: 
 11:10: 
 12:1,11: 
 13:9,12: 
 14:13: 
 15:14: 
 16:1: 
 17:15,16: 
 18:17: 
 19:18: 
 20:1: 
 21:19,20: 
 22:: 
 23:21,22: 
 24:: 
 25:24: 
 26:1,25: 
 27:23,26: 
 qed:27: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  truniALTVD 28727* 
The union of a class of transitive sets is transitive. The following
User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. truniALT 28361
is truniALTVD 28727 without virtual deductions and was automatically derived
from truniALTVD 28727.
1:: 
 2:: 
 3:2: 
 4:2: 
 5:4: 
 6:: 
 7:6: 
 8:6: 
 9:1,8: 
 10:8,9: 
 11:3,7,10: 
 12:11,8: 
 13:12: 
 14:13: 
 15:14: 
 16:5,15: 
 17:16: 
 18:17: 
 19:18: 
 qed:19: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  ee33VD 28728 
Nonvirtual deduction form of e33 28580. The following User's Proof is a
Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. ee33 28340
is ee33VD 28728 without virtual deductions and was automatically derived
from ee33VD 28728.
h1:: 
 h2:: 
 h3:: 
 4:1,3: 
 5:4: 
 6:2,5: 
 7:6: 
 8:7: 
 qed:8: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  trintALTVD 28729* 
The intersection of a class of transitive sets is transitive. Virtual
deduction proof of trintALT 28730.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. trintALT 28730
is trintALTVD 28729 without virtual deductions and was automatically derived
from trintALTVD 28729.
1:: 
 2:: 
 3:2: 
 4:2: 
 5:4: 
 6:5: 
 7:: 
 8:7,6: 
 9:7,1: 
 10:7,9: 
 11:10,3,8: 
 12:11: 
 13:12: 
 14:13: 
 15:3,14: 
 16:15: 
 17:16: 
 18:17: 
 qed:18: 

(Contributed by Alan Sare, 17Apr2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  trintALT 28730* 
The intersection of a class of transitive sets is transitive. Exercise
5(b) of [Enderton] p. 73. trintALT 28730 is an alternative proof of
trint 4130. trintALT 28730 is trintALTVD 28729 without virtual deductions and was
automatically derived from trintALTVD 28729 using the tools program
translate..without..overwriting.cmd and Metamath's minimize command.
(Contributed by Alan Sare, 17Apr2012.)
(Proof modification is discouraged.) (New usage is discouraged.)



Theorem  undif3VD 28731 
The first equality of Exercise 13 of [TakeutiZaring] p. 22. Virtual
deduction proof of undif3 3431.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. undif3 3431
is undif3VD 28731 without virtual deductions and was automatically derived
from undif3VD 28731.
1:: 
 2:: 
 3:2: 
 4:1,3: 
 5:: 
 6:5: 
 7:5: 
 8:6,7: 
 9:8: 
 10:: 
 11:10: 
 12:10: 
 13:11: 
 14:12: 
 15:13,14: 
 16:15: 
 17:9,16: 
 18:: 
 19:18: 
 20:18: 
 21:18: 
 22:21: 
 23:: 
 24:23: 
 25:24: 
 26:25: 
 27:10: 
 28:27: 
 29:: 
 30:29: 
 31:30: 
 32:31: 
 33:22,26: 
 34:28,32: 
 35:33,34: 
 36:: 
 37:36,35: 
 38:17,37: 
 39:: 
 40:39: 
 41:: 
 42:40,41: 
 43:: 
 44:43,42: 
 45:: 
 46:45,44: 
 47:4,38: 
 48:46,47: 
 49:48: 
 qed:49: 

(Contributed by Alan Sare, 17Apr2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcssVD 28732 
Virtual deduction proof of sbcss 3566.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. sbcss 3566
is sbcssVD 28732 without virtual deductions and was automatically derived
from sbcssVD 28732.
1:: 
 2:1: 
 3:1: 
 4:2,3: 
 5:1: 
 6:4,5: 
 7:6: 
 8:7: 
 9:1: 
 10:8,9: 
 11:: 
 110:11: 
 12:1,110: 
 13:10,12: 
 14:: 
 15:13,14: 
 qed:15: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbingVD 28733 
Virtual deduction proof of csbing 3378.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. csbing 3378
is csbingVD 28733 without virtual deductions and was automatically derived
from csbingVD 28733.
1:: 
 2:: 
 20:2: 
 30:1,20: 
 3:1,30: 
 4:1: 
 5:3,4: 
 6:1: 
 7:1: 
 8:6,7: 
 9:1: 
 10:9,8: 
 11:10: 
 12:11: 
 13:5,12: 
 14:: 
 15:13,14: 
 qed:15: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem5VD 28734* 
Virtual deduction proof of onfrALTlem5 28363.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem5 28363 is onfrALTlem5VD 28734 without virtual deductions and was
automatically derived
from onfrALTlem5VD 28734.
1:: 
 2:1: 
 3:2: 
 4:3: 
 5:: 
 6:4,5: 
 7:2: 
 8:: 
 9:8: 
 10:2,9: 
 11:7,10: 
 12:6,11: 
 13:2: 
 14:12,13: 
 15:2: 
 16:15,14: 
 17:2: 
 18:2: 
 19:2: 
 20:18,19: 
 21:17,20: 
 22:2: 
 23:2: 
 24:21,23: 
 25:22,24: 
 26:2: 
 27:25,26: 
 28:2: 
 29:27,28: 
 30:29: 
 31:30: 
 32:: 
 33:31,32: 
 34:2: 
 35:33,34: 
 36:: 
 37:36: 
 38:2,37: 
 39:35,38: 
 40:16,39: 
 41:2: 
 qed:40,41: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem4VD 28735* 
Virtual deduction proof of onfrALTlem4 28364.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. onfrALTlem4 28364
is onfrALTlem4VD 28735 without virtual deductions and was automatically
derived
from onfrALTlem4VD 28735.
1:: 
 2:1: 
 3:1: 
 4:1: 
 5:1: 
 6:4,5: 
 7:3,6: 
 8:1: 
 9:7,8: 
 10:2,9: 
 11:1: 
 12:11,10: 
 13:1: 
 qed:13,12: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem3VD 28736* 
Virtual deduction proof of onfrALTlem3 28365.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. onfrALTlem3 28365
is onfrALTlem3VD 28736 without virtual deductions and was automatically
derived
from onfrALTlem3VD 28736.
1:: 
 2:: 
 3:2: 
 4:1: 
 5:3,4: 
 6:5: 
 7:6: 
 8:: 
 9:7,8: 
 10:9: 
 11:10: 
 12:: 
 13:12,8: 
 14:13,11: 
 15:: 
 16:14,15: 
 17:: 
 18:2: 
 19:18: 
 20:17,19: 
 qed:16,20: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  simplbi2comgVD 28737 
Virtual deduction proof of simplbi2comg 1363.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. simplbi2comg 1363
is simplbi2comgVD 28737 without virtual deductions and was automatically
derived
from simplbi2comgVD 28737.
1:: 
 2:1: 
 3:2: 
 4:3: 
 qed:4: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem2VD 28738* 
Virtual deduction proof of onfrALTlem2 28367.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. onfrALTlem2 28367
is onfrALTlem2VD 28738 without virtual deductions and was automatically
derived
from onfrALTlem2VD 28738.
1:: 
 2:1: 
 3:2: 
 4:: 
 5:: 
 6:5: 
 7:4: 
 8:6,7: 
 9:8: 
 10:9: 
 11:1: 
 12:11: 
 13:2: 
 14:10,12,13: 
 15:3,14: 
 16:13,15: 
 