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Theorem fveqeq2d 5469
 Description: Equality deduction for function value. (Contributed by BJ, 30-Aug-2022.)
Hypothesis
Ref Expression
fveqeq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
fveqeq2d (𝜑 → ((𝐹𝐴) = 𝐶 ↔ (𝐹𝐵) = 𝐶))

Proof of Theorem fveqeq2d
StepHypRef Expression
1 fveqeq2d.1 . . 3 (𝜑𝐴 = 𝐵)
21fveq2d 5465 . 2 (𝜑 → (𝐹𝐴) = (𝐹𝐵))
32eqeq1d 2163 1 (𝜑 → ((𝐹𝐴) = 𝐶 ↔ (𝐹𝐵) = 𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   = wceq 1332  ‘cfv 5163 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-rex 2438  df-v 2711  df-un 3102  df-sn 3562  df-pr 3563  df-op 3565  df-uni 3769  df-br 3962  df-iota 5128  df-fv 5171 This theorem is referenced by:  fveqeq2  5470  enmkvlem  7083  algcvga  11899  pilem3  13043  nninfomni  13532
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