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Theorem funeqi 5219
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 5218 . 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 1348  Fun wfun 5192
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-in 3127  df-ss 3134  df-br 3990  df-opab 4051  df-rel 4618  df-cnv 4619  df-co 4620  df-fun 5200
This theorem is referenced by:  funmpt  5236  funmpt2  5237  funprg  5248  funtpg  5249  funtp  5251  funcnvuni  5267  f1cnvcnv  5414  f1co  5415  fun11iun  5463  f10  5476  funoprabg  5952  mpofun  5955  ovidig  5970  tposfun  6239  tfri1dALT  6330  tfrcl  6343  rdgfun  6352  frecfun  6374  frecfcllem  6383  th3qcor  6617  ssdomg  6756  sbthlem7  6940  sbthlemi8  6941  casefun  7062  caseinj  7066  djufun  7081  djuinj  7083  ctssdccl  7088  axaddf  7830  axmulf  7831  strleund  12506  strleun  12507  1strbas  12517  2strbasg  12519  2stropg  12520
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