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Theorem sbc2iegf 3007
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
sbc2iegf.1
sbc2iegf.2
sbc2iegf.3
sbc2iegf.4
Assertion
Ref Expression
sbc2iegf
Distinct variable groups:   ,,   ,   ,   ,
Allowed substitution hints:   (,)   (,)   ()   ()   ()

Proof of Theorem sbc2iegf
StepHypRef Expression
1 simpl 108 . 2
2 simpl 108 . . . 4
3 sbc2iegf.4 . . . . 5
43adantll 468 . . . 4
5 nfv 1508 . . . 4
6 sbc2iegf.2 . . . . 5
76a1i 9 . . . 4
82, 4, 5, 7sbciedf 2972 . . 3
98adantll 468 . 2
10 nfv 1508 . . 3
11 sbc2iegf.3 . . 3
1210, 11nfan 1545 . 2
13 sbc2iegf.1 . . 3
1413a1i 9 . 2
151, 9, 12, 14sbciedf 2972 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1335  wnf 1440   wcel 2128  wsbc 2937 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-sbc 2938 This theorem is referenced by:  sbc2ie  3008  opelopabaf  4232
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