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Theorem funeqi 5249
Description: Equality inference for the function predicate. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
funeqi.1  |-  A  =  B
Assertion
Ref Expression
funeqi  |-  ( Fun 
A  <->  Fun  B )

Proof of Theorem funeqi
StepHypRef Expression
1 funeqi.1 . 2  |-  A  =  B
2 funeq 5248 . 2  |-  ( A  =  B  ->  ( Fun  A  <->  Fun  B ) )
31, 2ax-mp 5 1  |-  ( Fun 
A  <->  Fun  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 105    = wceq 1363   Fun wfun 5222
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-in 3147  df-ss 3154  df-br 4016  df-opab 4077  df-rel 4645  df-cnv 4646  df-co 4647  df-fun 5230
This theorem is referenced by:  funmpt  5266  funmpt2  5267  funprg  5278  funtpg  5279  funtp  5281  funcnvuni  5297  f1cnvcnv  5444  f1co  5445  fun11iun  5494  f10  5507  funoprabg  5987  mpofun  5990  ovidig  6006  tposfun  6275  tfri1dALT  6366  tfrcl  6379  rdgfun  6388  frecfun  6410  frecfcllem  6419  th3qcor  6653  ssdomg  6792  sbthlem7  6976  sbthlemi8  6977  casefun  7098  caseinj  7102  djufun  7117  djuinj  7119  ctssdccl  7124  axaddf  7881  axmulf  7882  strleund  12577  strleun  12578  1strbas  12591  2strbasg  12593  2stropg  12594  lidlmex  13664
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