NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  elimhyp3v Unicode version

Theorem elimhyp3v 3712
Description: Eliminate a hypothesis containing 3 class variables. (Contributed by NM, 14-Aug-1999.)
Hypotheses
Ref Expression
elimhyp3v.1
elimhyp3v.2
elimhyp3v.3
elimhyp3v.4
elimhyp3v.5
elimhyp3v.6
elimhyp3v.7
Assertion
Ref Expression
elimhyp3v

Proof of Theorem elimhyp3v
StepHypRef Expression
1 iftrue 3668 . . . . . 6
21eqcomd 2358 . . . . 5
3 elimhyp3v.1 . . . . 5
42, 3syl 15 . . . 4
5 iftrue 3668 . . . . . 6
65eqcomd 2358 . . . . 5
7 elimhyp3v.2 . . . . 5
86, 7syl 15 . . . 4
9 iftrue 3668 . . . . . 6
109eqcomd 2358 . . . . 5
11 elimhyp3v.3 . . . . 5
1210, 11syl 15 . . . 4
134, 8, 123bitrd 270 . . 3
1413ibi 232 . 2
15 elimhyp3v.7 . . 3
16 iffalse 3669 . . . . . 6
1716eqcomd 2358 . . . . 5
18 elimhyp3v.4 . . . . 5
1917, 18syl 15 . . . 4
20 iffalse 3669 . . . . . 6
2120eqcomd 2358 . . . . 5
22 elimhyp3v.5 . . . . 5
2321, 22syl 15 . . . 4
24 iffalse 3669 . . . . . 6
2524eqcomd 2358 . . . . 5
26 elimhyp3v.6 . . . . 5
2725, 26syl 15 . . . 4
2819, 23, 273bitrd 270 . . 3
2915, 28mpbii 202 . 2
3014, 29pm2.61i 156 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wceq 1642  cif 3662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-if 3663
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator