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Theorem 2fveq3 5501
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 5496 . 2 (𝐴 = 𝐵 → (𝐺𝐴) = (𝐺𝐵))
21fveq2d 5500 1 (𝐴 = 𝐵 → (𝐹‘(𝐺𝐴)) = (𝐹‘(𝐺𝐵)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  cfv 5198
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206
This theorem is referenced by:  difinfsnlem  7076  ctssdclemn0  7087  cc2  7229  seq3f1olemqsum  10456  seq3f1oleml  10459  seq3f1o  10460  seq3homo  10466  seq3coll  10777  fsumf1o  11353  iserabs  11438  explecnv  11468  cvgratnnlemnexp  11487  cvgratnnlemmn  11488  fprodf1o  11551  alginv  12001  algcvg  12002  algcvga  12005  ctiunctlemu1st  12389  ctiunctlemu2nd  12390  ctiunctlemudc  12392  ctiunctlemfo  12394  subctctexmid  14034
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