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Theorem feq1d 5266
Description: Equality deduction for functions. (Contributed by NM, 19-Feb-2008.)
Hypothesis
Ref Expression
feq1d.1  |-  ( ph  ->  F  =  G )
Assertion
Ref Expression
feq1d  |-  ( ph  ->  ( F : A --> B 
<->  G : A --> B ) )

Proof of Theorem feq1d
StepHypRef Expression
1 feq1d.1 . 2  |-  ( ph  ->  F  =  G )
2 feq1 5262 . 2  |-  ( F  =  G  ->  ( F : A --> B  <->  G : A
--> B ) )
31, 2syl 14 1  |-  ( ph  ->  ( F : A --> B 
<->  G : A --> B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1332   -->wf 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-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-sn 3537  df-pr 3538  df-op 3540  df-br 3937  df-opab 3997  df-rel 4553  df-cnv 4554  df-co 4555  df-dm 4556  df-rn 4557  df-fun 5132  df-fn 5133  df-f 5134
This theorem is referenced by:  feq12d  5269  fco2  5296  fssres2  5307  fresin  5308  fmpt3d  5583  fmptco  5593  fressnfv  5614  off  6001  caofinvl  6011  f2ndf  6130  eroprf  6529  pmresg  6577  fseq1p1m1  9904  lmbr  12419  blfps  12615  blf  12616  dvmptclx  12886
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