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Theorem sbceqal 3214
 Description: Set theory version of sbeqal1 27576. (Contributed by Andrew Salmon, 28-Jun-2011.)
Assertion
Ref Expression
sbceqal
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem sbceqal
StepHypRef Expression
1 spsbc 3175 . 2
2 sbcimg 3204 . . 3
3 eqid 2438 . . . . 5
4 eqsbc3 3202 . . . . 5
53, 4mpbiri 226 . . . 4
6 pm5.5 328 . . . 4
75, 6syl 16 . . 3
8 eqsbc3 3202 . . 3
92, 7, 83bitrd 272 . 2
101, 9sylibd 207 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wceq 1653   wcel 1726  wsbc 3163 This theorem is referenced by:  sbeqalb  3215 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164
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