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Theorem 2fveq3 5539
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 5534 . 2 (𝐴 = 𝐵 → (𝐺𝐴) = (𝐺𝐵))
21fveq2d 5538 1 (𝐴 = 𝐵 → (𝐹‘(𝐺𝐴)) = (𝐹‘(𝐺𝐵)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364  cfv 5235
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5196  df-fv 5243
This theorem is referenced by:  difinfsnlem  7129  ctssdclemn0  7140  cc2  7297  seq3f1olemqsum  10533  seq3f1oleml  10536  seq3f1o  10537  seq3homo  10543  seq3coll  10857  fsumf1o  11433  iserabs  11518  explecnv  11548  cvgratnnlemnexp  11567  cvgratnnlemmn  11568  fprodf1o  11631  alginv  12082  algcvg  12083  algcvga  12086  ctiunctlemu1st  12488  ctiunctlemu2nd  12489  ctiunctlemudc  12491  ctiunctlemfo  12493  isunitd  13473  subctctexmid  15229
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