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Theorem eqsbc3 3367
Description: Substitution applied to an atomic wff. Set theory version of eqsb3 2577. (Contributed by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
eqsbc3
Distinct variable group:   ,

Proof of Theorem eqsbc3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq 3329 . 2
2 eqeq1 2461 . 2
3 sbsbc 3331 . . 3
4 eqsb3 2577 . . 3
53, 4bitr3i 251 . 2
61, 2, 5vtoclbg 3168 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327
This theorem is referenced by:  sbceqal  3383  eqsbc3r  3389  fmptsnd  6093  fvmptnn04if  19350  snfil  20365  iotavalb  31337  onfrALTlem5  33314  eqsbc3rVD  33640  onfrALTlem5VD  33685
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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