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Theorem fveq1d 5232
Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
fveq1d.1 (𝜑𝐹 = 𝐺)
Assertion
Ref Expression
fveq1d (𝜑 → (𝐹𝐴) = (𝐺𝐴))

Proof of Theorem fveq1d
StepHypRef Expression
1 fveq1d.1 . 2 (𝜑𝐹 = 𝐺)
2 fveq1 5229 . 2 (𝐹 = 𝐺 → (𝐹𝐴) = (𝐺𝐴))
31, 2syl 14 1 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285  cfv 4952
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 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-uni 3622  df-br 3806  df-iota 4917  df-fv 4960
This theorem is referenced by:  fveq12d  5236  funssfv  5252  csbfv2g  5263  fvmptd  5306  fvmpt2d  5310  mpteqb  5314  fvmptt  5315  fmptco  5383  fvunsng  5410  fvsng  5412  fsnunfv  5416  f1ocnvfv1  5469  f1ocnvfv2  5470  fcof1  5475  fcofo  5476  fnofval  5773  offval2  5778  ofrfval2  5779  caofinvl  5785  tfrlemi1  6002  rdg0g  6058  freceq1  6062  oav  6119  omv  6120  oeiv  6121  fseq1p1m1  9257  iseqeq3  9596  iseqid  9633  iseqz  9636  serige0  9640  serile  9641  expival  9645  ibcval5  9857  bcn2  9858  shftcan1  9941  shftcan2  9942  shftvalg  9943  shftval4g  9944  climshft2  10364  iserile  10399  sumeq2d  10415  sumeq2  10416
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