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Theorem funeq 5152
 Description: Equality theorem for function predicate. (Contributed by NM, 16-Aug-1994.)
Assertion
Ref Expression
funeq

Proof of Theorem funeq
StepHypRef Expression
1 eqimss2 3158 . . 3
2 funss 5151 . . 3
31, 2syl 14 . 2
4 eqimss 3157 . . 3
5 funss 5151 . . 3
64, 5syl 14 . 2
73, 6impbid 128 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332   wss 3077   wfun 5126 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-in 3083  df-ss 3090  df-br 3939  df-opab 3999  df-rel 4555  df-cnv 4556  df-co 4557  df-fun 5134 This theorem is referenced by:  funeqi  5153  funeqd  5154  fununi  5200  funcnvuni  5201  cnvresid  5206  fneq1  5220  elpmg  6567  fundmeng  6710
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