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Theorem sbc5 3070
 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 3055 . 2
2 exsimpl 1592 . . 3
3 isset 2863 . . 3
42, 3sylibr 203 . 2
5 dfsbcq2 3049 . . 3
6 eqeq2 2362 . . . . 5
76anbi1d 685 . . . 4
87exbidv 1626 . . 3
9 sb5 2100 . . 3
105, 8, 9vtoclbg 2915 . 2
111, 4, 10pm5.21nii 342 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541   wceq 1642  wsb 1648   wcel 1710  cvv 2859  wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbc6g  3071  sbc7  3073  sbciegft  3076  sbccomlem  3116  csb2  3138  rexsns  3764
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