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Theorem funeqi 5022
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 5021 . 2  |-  ( A  =  B  ->  ( Fun  A  <->  Fun  B ) )
31, 2ax-mp 7 1  |-  ( Fun 
A  <->  Fun  B )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1289   Fun wfun 4996
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-in 3003  df-ss 3010  df-br 3838  df-opab 3892  df-rel 4435  df-cnv 4436  df-co 4437  df-fun 5004
This theorem is referenced by:  funmpt  5038  funmpt2  5039  funprg  5050  funtpg  5051  funtp  5053  funcnvuni  5069  f1cnvcnv  5211  f1co  5212  fun11iun  5258  f10  5271  funoprabg  5726  mpt2fun  5729  ovidig  5744  tposfun  6007  tfri1dALT  6098  tfrcl  6111  rdgfun  6120  frecfun  6142  frecfcllem  6151  th3qcor  6376  ssdomg  6475  sbthlem7  6651  sbthlemi8  6652  casefun  6755  caseinj  6759  djufun  6763  djuinj  6765
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