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Theorem fveq12d 5130
Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008.)
Hypotheses
Ref Expression
fveq12d.1 (φ𝐹 = 𝐺)
fveq12d.2 (φA = B)
Assertion
Ref Expression
fveq12d (φ → (𝐹A) = (𝐺B))

Proof of Theorem fveq12d
StepHypRef Expression
1 fveq12d.1 . . 3 (φ𝐹 = 𝐺)
21fveq1d 5126 . 2 (φ → (𝐹A) = (𝐺A))
3 fveq12d.2 . . 3 (φA = B)
43fveq2d 5128 . 2 (φ → (𝐺A) = (𝐺B))
52, 4eqtrd 2072 1 (φ → (𝐹A) = (𝐺B))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1243  cfv 4848
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-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2309  df-v 2556  df-un 2919  df-sn 3376  df-pr 3377  df-op 3379  df-uni 3575  df-br 3759  df-iota 4813  df-fv 4856
This theorem is referenced by:  nffvd  5133  fvsng  5305  tfrlem3ag  5869  tfrlem3a  5870  tfrlemi1  5891
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