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Theorem funeqd 4947
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 4945 . 2  |-  ( A  =  B  ->  ( Fun  A  <->  Fun  B ) )
31, 2syl 14 1  |-  ( ph  ->  ( Fun  A  <->  Fun  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    = wceq 1285   Fun wfun 4920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-in 2980  df-ss 2987  df-br 3788  df-opab 3842  df-rel 4372  df-cnv 4373  df-co 4374  df-fun 4928
This theorem is referenced by:  funopg  4958  funsng  4970  funcnvuni  4993  f1eq1  5112  frecuzrdgtclt  9492  shftfn  9839
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