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Theorem seeq1 4123
 Description: Equality theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.)
Assertion
Ref Expression
seeq1 Se Se

Proof of Theorem seeq1
StepHypRef Expression
1 eqimss2 3062 . . 3
2 sess1 4121 . . 3 Se Se
31, 2syl 14 . 2 Se Se
4 eqimss 3061 . . 3
5 sess1 4121 . . 3 Se Se
64, 5syl 14 . 2 Se Se
73, 6impbid 127 1 Se Se
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wss 2983   Se wse 4113 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  ax-sep 3917 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-ral 2358  df-rab 2362  df-v 2612  df-in 2989  df-ss 2996  df-br 3807  df-se 4117 This theorem is referenced by: (None)
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