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Theorem 2fveq3 5520
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 5515 . 2 (𝐴 = 𝐵 → (𝐺𝐴) = (𝐺𝐵))
21fveq2d 5519 1 (𝐴 = 𝐵 → (𝐹‘(𝐺𝐴)) = (𝐹‘(𝐺𝐵)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  cfv 5216
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 2739  df-un 3133  df-sn 3598  df-pr 3599  df-op 3601  df-uni 3810  df-br 4004  df-iota 5178  df-fv 5224
This theorem is referenced by:  difinfsnlem  7097  ctssdclemn0  7108  cc2  7265  seq3f1olemqsum  10499  seq3f1oleml  10502  seq3f1o  10503  seq3homo  10509  seq3coll  10821  fsumf1o  11397  iserabs  11482  explecnv  11512  cvgratnnlemnexp  11531  cvgratnnlemmn  11532  fprodf1o  11595  alginv  12046  algcvg  12047  algcvga  12050  ctiunctlemu1st  12434  ctiunctlemu2nd  12435  ctiunctlemudc  12437  ctiunctlemfo  12439  isunitd  13273  subctctexmid  14720
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