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Theorem fneq1i 5674
Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq1i.1  |-  F  =  G
Assertion
Ref Expression
fneq1i  |-  ( F  Fn  A  <->  G  Fn  A )

Proof of Theorem fneq1i
StepHypRef Expression
1 fneq1i.1 . 2  |-  F  =  G
2 fneq1 5668 . 2  |-  ( F  =  G  ->  ( F  Fn  A  <->  G  Fn  A ) )
31, 2ax-mp 5 1  |-  ( F  Fn  A  <->  G  Fn  A )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    = wceq 1379    Fn wfn 5582
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-fun 5589  df-fn 5590
This theorem is referenced by:  fnunsn  5687  fnopabg  5703  f1oun  5834  f1oi  5850  f1osn  5852  ovid  6402  curry1  6875  curry2  6878  tfrlem10  7056  tfr1  7066  seqomlem2  7116  seqomlem3  7117  seqomlem4  7118  fnseqom  7120  unblem4  7774  r1fnon  8184  alephfnon  8445  alephfplem4  8487  alephfp  8488  cfsmolem  8649  infpssrlem3  8684  compssiso  8753  hsmexlem5  8809  axdclem2  8899  wunex2  9115  wuncval2  9124  om2uzrani  12030  om2uzf1oi  12031  uzrdglem  12035  uzrdgfni  12036  uzrdg0i  12037  hashkf  12374  dmaf  15233  cdaf  15234  prdsinvlem  15985  pws1  17061  frlmphl  18595  ovolunlem1  21659  0plef  21830  0pledm  21831  itg1ge0  21844  itg1addlem4  21857  mbfi1fseqlem5  21877  itg2addlem  21916  qaa  22469  2trllemD  24251  eupap1  24668  ghgrp  25062  0vfval  25191  mptfnf  27187  xrge0pluscn  27574  wfrlem5  28940  wfrlem13  28948  frrlem5  28984  fullfunfnv  29189  neibastop2lem  29797  fourierdlem42  31465  bnj927  32915  bnj535  33036
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