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Theorem fveq1d 5180
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 5177 . 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 1243   ` cfv 4902
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910
This theorem is referenced by:  fveq12d  5184  funssfv  5199  csbfv2g  5210  fvmptd  5253  fvmpt2d  5257  mpteqb  5261  fvmptt  5262  fmptco  5330  fvunsng  5357  fvsng  5359  fsnunfv  5363  f1ocnvfv1  5417  f1ocnvfv2  5418  fcof1  5423  fcofo  5424  fnofval  5721  offval2  5726  ofrfval2  5727  caofinvl  5733  tfrlemi1  5946  rdg0g  5975  freceq1  5979  oav  6034  omv  6035  oeiv  6036  fseq1p1m1  8956  iseqeq3  9216  iseqid  9247  serige0  9252  serile  9253  expival  9257  shftcan1  9435  shftcan2  9436  shftvalg  9437  shftval4g  9438  climshft2  9827  iserile  9862
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