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Theorem sbceqal 3097
 Description: Set theory version of sbeqal1 in set.mm. (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 3058 . 2
2 sbcimg 3087 . . 3
3 eqid 2353 . . . . 5
4 eqsbc3 3085 . . . . 5
53, 4mpbiri 224 . . . 4
6 pm5.5 326 . . . 4
75, 6syl 15 . . 3
8 eqsbc3 3085 . . 3
92, 7, 83bitrd 270 . 2
101, 9sylibd 205 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710  wsbc 3046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbeqalb  3098
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