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Theorem eqsbc3 3200
 Description: Substitution applied to an atomic wff. Set theory version of eqsb3 2537. (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 3163 . 2
2 eqeq1 2442 . 2
3 sbsbc 3165 . . 3
4 eqsb3 2537 . . 3
53, 4bitr3i 243 . 2
61, 2, 5vtoclbg 3012 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652  wsb 1658   wcel 1725  wsbc 3161 This theorem is referenced by:  sbceqal  3212  eqsbc3r  3218  snfil  17896  iotavalb  27607  onfrALTlem5  28628  eqsbc3rVD  28952  onfrALTlem5VD  28997 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162
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