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Theorem eqsbc3 2802
 Description: Substitution applied to an atomic wff. Set theory version of eqsb3 2141. (Contributed by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
eqsbc3
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem eqsbc3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq 2766 . 2
2 eqeq1 2046 . 2
3 sbsbc 2768 . . 3
4 eqsb3 2141 . . 3
53, 4bitr3i 175 . 2
61, 2, 5vtoclbg 2614 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  wsb 1645  wsbc 2764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765 This theorem is referenced by:  sbceqal  2814  eqsbc3r  2819
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