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Theorem sbc5 2932
 Description: An equivalence for class substitution. (Contributed by NM, 23-Aug-1993.) (Revised by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
sbc5
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem sbc5
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 2917 . 2
2 exsimpl 1596 . . 3
3 isset 2692 . . 3
42, 3sylibr 133 . 2
5 dfsbcq2 2912 . . 3
6 eqeq2 2149 . . . . 5
76anbi1d 460 . . . 4
87exbidv 1797 . . 3
9 sb5 1859 . . 3
105, 8, 9vtoclbg 2747 . 2
111, 4, 10pm5.21nii 693 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wceq 1331  wex 1468   wcel 1480  wsb 1735  cvv 2686  wsbc 2909 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910 This theorem is referenced by:  sbc6g  2933  sbc7  2935  sbciegft  2939  sbccomlem  2983  csb2  3005  rexsns  3563
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