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Theorem funeq 5612
Description: Equality theorem for function predicate. (Contributed by NM, 16-Aug-1994.)
Assertion
Ref Expression
funeq

Proof of Theorem funeq
StepHypRef Expression
1 eqimss2 3556 . . 3
2 funss 5611 . . 3
31, 2syl 16 . 2
4 eqimss 3555 . . 3
5 funss 5611 . . 3
64, 5syl 16 . 2
73, 6impbid 191 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  C_wss 3475  Funwfun 5587
This theorem is referenced by:  funeqi  5613  funeqd  5614  fununi  5659  cnvresid  5663  fneq1  5674  nvof1o  6186  funcnvuni  6753  elpmg  7454  fundmeng  7610  isfsupp  7853  dfac9  8537  axdc3lem2  8852  frlmphllem  18811  locfinreflem  27843  orvcval  28396  elfunsg  29566  bnj1379  33889  bnj1385  33891  bnj1497  34116
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-in 3482  df-ss 3489  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-fun 5595
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