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Theorem funeqd 5467
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 5465 . 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 1652   Fun wfun 5440
This theorem is referenced by:  funopg  5477  funsng  5489  funcnvuni  5510  f1eq1  5626  shftfn  11880  isstruct2  13470  strle1  13552  monfval  13950  ismon  13951  monpropd  13955  isepi  13958  isfth  14103  acsficl2d  14594  istrl  21529  ispth  21560  isspth  21561  0spth  21563  1pthonlem1  21581  constr2spthlem1  21586  2pthlem1  21587  constr2pth  21593  constr3pthlem2  21635  ajfun  22354  sitgf  24652  dfateq12d  27960  afvres  28003  usgra2pthspth  28258
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-in 3319  df-ss 3326  df-br 4205  df-opab 4259  df-rel 4877  df-cnv 4878  df-co 4879  df-fun 5448
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