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Theorem fneq1i 5354
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 5349 . 2  |-  ( F  =  G  ->  ( F  Fn  A  <->  G  Fn  A ) )
31, 2ax-mp 8 1  |-  ( F  Fn  A  <->  G  Fn  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1632    Fn wfn 5266
This theorem is referenced by:  fnunsn  5367  fnopabg  5383  f1oun  5508  f1oi  5527  f1osn  5529  ovid  5980  curry1  6226  curry2  6229  tfrlem10  6419  tfr1  6429  seqomlem2  6479  seqomlem3  6480  seqomlem4  6481  fnseqom  6483  abianfp  6487  unblem4  7128  r1fnon  7455  alephfnon  7708  alephfplem4  7750  alephfp  7751  cfsmolem  7912  infpssrlem3  7947  compssiso  8016  hsmexlem5  8072  axdclem2  8163  wunex2  8376  wuncval2  8385  om2uzrani  11031  om2uzf1oi  11032  uzrdglem  11036  uzrdgfni  11037  uzrdg0i  11038  hashkf  11355  dmaf  13897  cdaf  13898  prdsinvlem  14619  pws1  15415  ovolunlem1  18872  0plef  19043  0pledm  19044  itg1ge0  19057  itg1addlem4  19070  mbfi1fseqlem5  19090  itg2addlem  19129  qaa  19719  ghgrp  21051  0vfval  21178  mptfnf  23241  xrge0pluscn  23337  eupap1  23915  wfrlem5  24331  wfrlem13  24339  frrlem5  24356  fullfunfnv  24556  trooo  25497  trinv  25498  neibastop2lem  26412  bnj927  29116  bnj535  29238
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-fun 5273  df-fn 5274
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