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Theorem fvoveq1 5713
Description: Equality theorem for nested function and operation value. Closed form of fvoveq1d 5712. (Contributed by AV, 23-Jul-2022.)
Assertion
Ref Expression
fvoveq1 (𝐴 = 𝐵 → (𝐹‘(𝐴𝑂𝐶)) = (𝐹‘(𝐵𝑂𝐶)))

Proof of Theorem fvoveq1
StepHypRef Expression
1 id 19 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
21fvoveq1d 5712 1 (𝐴 = 𝐵 → (𝐹‘(𝐴𝑂𝐶)) = (𝐹‘(𝐵𝑂𝐶)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1296  cfv 5049  (class class class)co 5690
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 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rex 2376  df-v 2635  df-un 3017  df-sn 3472  df-pr 3473  df-op 3475  df-uni 3676  df-br 3868  df-iota 5014  df-fv 5057  df-ov 5693
This theorem is referenced by:  seq3val  10020  seqf  10026  seq3p1  10030  seq3shft2  10038  seq3f1olemqsum  10066  facp1  10269  serf0  10910  fsumrelem  11029  mertenslemub  11092  mertenslemi1  11093  mertenslem2  11094  mertensabs  11095  comet  12300  mulc1cncf  12357  cncfco  12359
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