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Theorem 2fveq3 5521
Description: Equality theorem for nested function values. (Contributed by AV, 14-Aug-2022.)
Assertion
Ref Expression
2fveq3 (𝐴 = 𝐵 → (𝐹‘(𝐺𝐴)) = (𝐹‘(𝐺𝐵)))

Proof of Theorem 2fveq3
StepHypRef Expression
1 fveq2 5516 . 2 (𝐴 = 𝐵 → (𝐺𝐴) = (𝐺𝐵))
21fveq2d 5520 1 (𝐴 = 𝐵 → (𝐹‘(𝐺𝐴)) = (𝐹‘(𝐺𝐵)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  cfv 5217
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2740  df-un 3134  df-sn 3599  df-pr 3600  df-op 3602  df-uni 3811  df-br 4005  df-iota 5179  df-fv 5225
This theorem is referenced by:  difinfsnlem  7098  ctssdclemn0  7109  cc2  7266  seq3f1olemqsum  10500  seq3f1oleml  10503  seq3f1o  10504  seq3homo  10510  seq3coll  10822  fsumf1o  11398  iserabs  11483  explecnv  11513  cvgratnnlemnexp  11532  cvgratnnlemmn  11533  fprodf1o  11596  alginv  12047  algcvg  12048  algcvga  12051  ctiunctlemu1st  12435  ctiunctlemu2nd  12436  ctiunctlemudc  12438  ctiunctlemfo  12440  isunitd  13275  subctctexmid  14753
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