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Theorem fvoveq1d 5796
Description: Equality deduction for nested function and operation value. (Contributed by AV, 23-Jul-2022.)
Hypothesis
Ref Expression
fvoveq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
fvoveq1d (𝜑 → (𝐹‘(𝐴𝑂𝐶)) = (𝐹‘(𝐵𝑂𝐶)))

Proof of Theorem fvoveq1d
StepHypRef Expression
1 fvoveq1d.1 . . 3 (𝜑𝐴 = 𝐵)
21oveq1d 5789 . 2 (𝜑 → (𝐴𝑂𝐶) = (𝐵𝑂𝐶))
32fveq2d 5425 1 (𝜑 → (𝐹‘(𝐴𝑂𝐶)) = (𝐹‘(𝐵𝑂𝐶)))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1331  cfv 5123  (class class class)co 5774
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777
This theorem is referenced by:  fvoveq1  5797  imbrov2fvoveq  5799  seqvalcd  10239  mulc1cncf  12755  mulcncflem  12769  mulcncf  12770  limccl  12807  ellimc3apf  12808  limcdifap  12810  limcmpted  12811  limcresi  12814  limccoap  12826  dveflem  12865
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