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Theorem sbceqal 2878
 Description: A variation of extensionality for classes. (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 2835 . 2
2 sbcimg 2864 . . 3
3 eqid 2083 . . . . 5
4 eqsbc3 2862 . . . . 5
53, 4mpbiri 166 . . . 4
6 pm5.5 240 . . . 4
75, 6syl 14 . . 3
8 eqsbc3 2862 . . 3
92, 7, 83bitrd 212 . 2
101, 9sylibd 147 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283   wceq 1285   wcel 1434  wsbc 2824 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-sbc 2825 This theorem is referenced by:  sbeqalb  2879  snsssn  3573
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