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Theorem funeqd 5408
Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013.)
Hypothesis
Ref Expression
funeqd.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
funeqd  |-  ( ph  ->  ( Fun  A  <->  Fun  B ) )

Proof of Theorem funeqd
StepHypRef Expression
1 funeqd.1 . 2  |-  ( ph  ->  A  =  B )
2 funeq 5406 . 2  |-  ( A  =  B  ->  ( Fun  A  <->  Fun  B ) )
31, 2syl 16 1  |-  ( ph  ->  ( Fun  A  <->  Fun  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    = wceq 1649   Fun wfun 5381
This theorem is referenced by:  funopg  5418  funsng  5430  funcnvuni  5451  f1eq1  5567  shftfn  11808  isstruct2  13398  strle1  13480  monfval  13878  ismon  13879  monpropd  13883  isepi  13886  isfth  14031  acsficl2d  14522  istrl  21394  ispth  21415  isspth  21416  0spth  21418  1pthonlem1  21430  2pthonlem1  21440  constr3pthlem2  21484  ajfun  22203  dfateq12d  27655  afvres  27698
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-in 3263  df-ss 3270  df-br 4147  df-opab 4201  df-rel 4818  df-cnv 4819  df-co 4820  df-fun 5389
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