ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  funeqi GIF version

Theorem funeqi 5114
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 5113 . 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 1316  Fun wfun 5087
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-in 3047  df-ss 3054  df-br 3900  df-opab 3960  df-rel 4516  df-cnv 4517  df-co 4518  df-fun 5095
This theorem is referenced by:  funmpt  5131  funmpt2  5132  funprg  5143  funtpg  5144  funtp  5146  funcnvuni  5162  f1cnvcnv  5309  f1co  5310  fun11iun  5356  f10  5369  funoprabg  5838  mpofun  5841  ovidig  5856  tposfun  6125  tfri1dALT  6216  tfrcl  6229  rdgfun  6238  frecfun  6260  frecfcllem  6269  th3qcor  6501  ssdomg  6640  sbthlem7  6819  sbthlemi8  6820  casefun  6938  caseinj  6942  djufun  6957  djuinj  6959  ctssdccl  6964  axaddf  7644  axmulf  7645  strleund  11974  strleun  11975  1strbas  11985  2strbasg  11987  2stropg  11988
  Copyright terms: Public domain W3C validator