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Theorem eqsbc3 3064
 Description: Substitution applied to an atomic wff. Set theory version of eqsb3 2417. (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 3027 . 2
2 eqeq1 2322 . 2
3 sbsbc 3029 . . 3
4 eqsb3 2417 . . 3
53, 4bitr3i 242 . 2
61, 2, 5vtoclbg 2878 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1633  wsb 1639   wcel 1701  wsbc 3025 This theorem is referenced by:  sbceqal  3076  eqsbc3r  3082  snfil  17611  iotavalb  26778  onfrALTlem5  27801  eqsbc3rVD  28127  onfrALTlem5VD  28172 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-v 2824  df-sbc 3026
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