Theorem fveq1d 5200

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

Step	Hyp	Ref	Expression
1		fveq1d.1	. 2 |- ( ph -> F = G )
2		fveq1 5197	. 2 |- ( F = G -> ( F ` A ) = ( G ` A ) )
3	1, 2	syl 14	1 |- ( ph -> ( F ` A ) = ( G ` A ) )

Syntax hints:   -> wi 4   = wceq 1284   ` cfv 4922

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-uni 3602  df-br 3786  df-iota 4887  df-fv 4930

This theorem is referenced by:  fveq12d  5204  funssfv  5220  csbfv2g  5231  fvmptd  5274  fvmpt2d  5278  mpteqb  5282  fvmptt  5283  fmptco  5351  fvunsng  5378  fvsng  5380  fsnunfv  5384  f1ocnvfv1  5437  f1ocnvfv2  5438  fcof1  5443  fcofo  5444  fnofval  5741  offval2  5746  ofrfval2  5747  caofinvl  5753  tfrlemi1  5969  rdg0g  5998  freceq1  6002  oav  6057  omv  6058  oeiv  6059  fseq1p1m1  9111  iseqeq3  9436  iseqid  9467  iseqz  9469  serige0  9473  serile  9474  expival  9478  ibcval5  9690  bcn2  9691  shftcan1  9722  shftcan2  9723  shftvalg  9724  shftval4g  9725  climshft2  10145  iserile  10180