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Theorem feq1i 5201
Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
feq1i.1  |-  F  =  G
Assertion
Ref Expression
feq1i  |-  ( F : A --> B  <->  G : A
--> B )

Proof of Theorem feq1i
StepHypRef Expression
1 feq1i.1 . 2  |-  F  =  G
2 feq1 5191 . 2  |-  ( F  =  G  ->  ( F : A --> B  <->  G : A
--> B ) )
31, 2ax-mp 7 1  |-  ( F : A --> B  <->  G : A
--> B )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1299   -->wf 5055
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-sn 3480  df-pr 3481  df-op 3483  df-br 3876  df-opab 3930  df-rel 4484  df-cnv 4485  df-co 4486  df-dm 4487  df-rn 4488  df-fun 5061  df-fn 5062  df-f 5063
This theorem is referenced by:  ftpg  5536  frecfcllem  6231  frecsuclem  6233  omp1eomlem  6894  frecuzrdgrcl  10024  frecuzrdgrclt  10029  fxnn0nninf  10052  resqrexlemf  10619  algrf  11519  ennnfonelemh  11709
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