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Theorem funeqi 5049
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 5048 . 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 104   = wceq 1290  Fun wfun 5022
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-in 3006  df-ss 3013  df-br 3852  df-opab 3906  df-rel 4459  df-cnv 4460  df-co 4461  df-fun 5030
This theorem is referenced by:  funmpt  5065  funmpt2  5066  funprg  5077  funtpg  5078  funtp  5080  funcnvuni  5096  f1cnvcnv  5240  f1co  5241  fun11iun  5287  f10  5300  funoprabg  5758  mpt2fun  5761  ovidig  5776  tposfun  6039  tfri1dALT  6130  tfrcl  6143  rdgfun  6152  frecfun  6174  frecfcllem  6183  th3qcor  6410  ssdomg  6549  sbthlem7  6726  sbthlemi8  6727  casefun  6830  caseinj  6834  djufun  6840  djuinj  6842  strleund  11643  strleun  11644  1strbas  11654  2strbasg  11656  2stropg  11657
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