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Theorem funeqi 5036
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 5035 . 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 5009
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 3005  df-ss 3012  df-br 3846  df-opab 3900  df-rel 4445  df-cnv 4446  df-co 4447  df-fun 5017
This theorem is referenced by:  funmpt  5052  funmpt2  5053  funprg  5064  funtpg  5065  funtp  5067  funcnvuni  5083  f1cnvcnv  5227  f1co  5228  fun11iun  5274  f10  5287  funoprabg  5744  mpt2fun  5747  ovidig  5762  tposfun  6025  tfri1dALT  6116  tfrcl  6129  rdgfun  6138  frecfun  6160  frecfcllem  6169  th3qcor  6394  ssdomg  6493  sbthlem7  6670  sbthlemi8  6671  casefun  6774  caseinj  6778  djufun  6782  djuinj  6784
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