ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fveq1d Unicode version

Theorem fveq1d 5211
Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
fveq1d.1  |-  ( ph  ->  F  =  G )
Assertion
Ref Expression
fveq1d  |-  ( ph  ->  ( F `  A
)  =  ( G `
 A ) )

Proof of Theorem fveq1d
StepHypRef Expression
1 fveq1d.1 . 2  |-  ( ph  ->  F  =  G )
2 fveq1 5208 . 2  |-  ( F  =  G  ->  ( F `  A )  =  ( G `  A ) )
31, 2syl 14 1  |-  ( ph  ->  ( F `  A
)  =  ( G `
 A ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285   ` cfv 4932
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-uni 3610  df-br 3794  df-iota 4897  df-fv 4940
This theorem is referenced by:  fveq12d  5215  funssfv  5231  csbfv2g  5242  fvmptd  5285  fvmpt2d  5289  mpteqb  5293  fvmptt  5294  fmptco  5362  fvunsng  5389  fvsng  5391  fsnunfv  5395  f1ocnvfv1  5448  f1ocnvfv2  5449  fcof1  5454  fcofo  5455  fnofval  5752  offval2  5757  ofrfval2  5758  caofinvl  5764  tfrlemi1  5981  rdg0g  6037  freceq1  6041  oav  6098  omv  6099  oeiv  6100  fseq1p1m1  9187  iseqeq3  9526  iseqid  9563  iseqz  9566  serige0  9570  serile  9571  expival  9575  ibcval5  9787  bcn2  9788  shftcan1  9860  shftcan2  9861  shftvalg  9862  shftval4g  9863  climshft2  10283  iserile  10318  sumeq2d  10334  sumeq2  10335
  Copyright terms: Public domain W3C validator