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Theorem fvoveq1 5691
Description: Equality theorem for nested function and operation value. Closed form of fvoveq1d 5690. (Contributed by AV, 23-Jul-2022.)
Assertion
Ref Expression
fvoveq1  |-  ( A  =  B  ->  ( F `  ( A O C ) )  =  ( F `  ( B O C ) ) )

Proof of Theorem fvoveq1
StepHypRef Expression
1 id 19 . 2  |-  ( A  =  B  ->  A  =  B )
21fvoveq1d 5690 1  |-  ( A  =  B  ->  ( F `  ( A O C ) )  =  ( F `  ( B O C ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1290   ` cfv 5030  (class class class)co 5668
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 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-v 2624  df-un 3006  df-sn 3458  df-pr 3459  df-op 3461  df-uni 3662  df-br 3854  df-iota 4995  df-fv 5038  df-ov 5671
This theorem is referenced by:  seq3val  9937  seqf  9943  seq3p1  9947  seq3f1olemqsum  9992  serf0  10804  fsumrelem  10928  mertenslemub  10991  mertenslemi1  10992  mertenslem2  10993  mertensabs  10994  mulc1cncf  11949  cncfco  11951
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