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Theorem sbc2ie 2894
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by NM, 16-Dec-2008.) (Revised by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
sbc2ie.1
sbc2ie.2
sbc2ie.3
Assertion
Ref Expression
sbc2ie
Distinct variable groups:   ,,   ,   ,,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbc2ie
StepHypRef Expression
1 sbc2ie.1 . 2
2 sbc2ie.2 . 2
3 nfv 1462 . . 3
4 nfv 1462 . . 3
52nfth 1394 . . 3
6 sbc2ie.3 . . 3
73, 4, 5, 6sbc2iegf 2893 . 2
81, 2, 7mp2an 417 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  cvv 2610  wsbc 2824 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-sbc 2825 This theorem is referenced by:  sbc3ie  2896
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