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Theorem 2fveq3 5358
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 5353 . 2 (𝐴 = 𝐵 → (𝐺𝐴) = (𝐺𝐵))
21fveq2d 5357 1 (𝐴 = 𝐵 → (𝐹‘(𝐺𝐴)) = (𝐹‘(𝐺𝐵)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1299  cfv 5059
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-rex 2381  df-v 2643  df-un 3025  df-sn 3480  df-pr 3481  df-op 3483  df-uni 3684  df-br 3876  df-iota 5024  df-fv 5067
This theorem is referenced by:  difinfsnlem  6899  ctssdclemn0  6910  seq3f1olemqsum  10114  seq3f1oleml  10117  seq3f1o  10118  seq3homo  10124  seq3coll  10426  fsumf1o  10998  iserabs  11083  explecnv  11113  cvgratnnlemnexp  11132  cvgratnnlemmn  11133  alginv  11521  algcvg  11522  algcvga  11525
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