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Theorem fveq1d 5123
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 5120 . 2 (𝐹 = 𝐺 → (𝐹A) = (𝐺A))
31, 2syl 14 1 (φ → (𝐹A) = (𝐺A))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  cfv 4845
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853
This theorem is referenced by:  fveq12d  5127  funssfv  5142  csbfv2g  5153  fvmptd  5196  fvmpt2d  5200  mpteqb  5204  fvmptt  5205  fmptco  5273  fvunsng  5300  fvsng  5302  fsnunfv  5306  f1ocnvfv1  5360  f1ocnvfv2  5361  fcof1  5366  fcofo  5367  fnofval  5663  offval2  5668  ofrfval2  5669  caofinvl  5675  tfrlemi1  5887  rdg0g  5915  freceq1  5919  oav  5973  omv  5974  oeiv  5975  fseq1p1m1  8686  iseqeq3  8856  expival  8871
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