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Theorem funeqi 5194
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 5193 . 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 104   = wceq 1335  Fun wfun 5167
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-in 3108  df-ss 3115  df-br 3968  df-opab 4029  df-rel 4596  df-cnv 4597  df-co 4598  df-fun 5175
This theorem is referenced by:  funmpt  5211  funmpt2  5212  funprg  5223  funtpg  5224  funtp  5226  funcnvuni  5242  f1cnvcnv  5389  f1co  5390  fun11iun  5438  f10  5451  funoprabg  5923  mpofun  5926  ovidig  5941  tposfun  6210  tfri1dALT  6301  tfrcl  6314  rdgfun  6323  frecfun  6345  frecfcllem  6354  th3qcor  6587  ssdomg  6726  sbthlem7  6910  sbthlemi8  6911  casefun  7032  caseinj  7036  djufun  7051  djuinj  7053  ctssdccl  7058  axaddf  7791  axmulf  7792  strleund  12374  strleun  12375  1strbas  12385  2strbasg  12387  2stropg  12388
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