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Theorem fveqeq2 5526
Description: Equality deduction for function value. (Contributed by BJ, 31-Aug-2022.)
Assertion
Ref Expression
fveqeq2 (𝐴 = 𝐵 → ((𝐹𝐴) = 𝐶 ↔ (𝐹𝐵) = 𝐶))

Proof of Theorem fveqeq2
StepHypRef Expression
1 id 19 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
21fveqeq2d 5525 1 (𝐴 = 𝐵 → ((𝐹𝐴) = 𝐶 ↔ (𝐹𝐵) = 𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105   = wceq 1353  cfv 5218
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2741  df-un 3135  df-sn 3600  df-pr 3601  df-op 3603  df-uni 3812  df-br 4006  df-iota 5180  df-fv 5226
This theorem is referenced by:  nnnninfeq2  7129  fodjum  7146  fodju0  7147  fodjuomnilemres  7148  fodjumkvlemres  7159  fodjumkv  7160  enmkvlem  7161  enwomnilem  7169  nninfwlporlemd  7172  nninfwlpoimlemginf  7176  nninfwlpoim  7178  seq3id3  10509  seq3id2  10511  seq3z  10513  fsum3cvg  11388  summodclem2a  11391  fproddccvg  11582  algfx  12054  ennnfonelemim  12427  reeff1oleme  14278  sin0pilem2  14288  bj-charfunbi  14648  nninfomnilem  14852  trilpolemlt1  14874  redcwlpolemeq1  14887  nconstwlpolem0  14896  nconstwlpolem  14898  neapmkvlem  14900
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