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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  7130  fodjum  7147  fodju0  7148  fodjuomnilemres  7149  fodjumkvlemres  7160  fodjumkv  7161  enmkvlem  7162  enwomnilem  7170  nninfwlporlemd  7173  nninfwlpoimlemginf  7177  nninfwlpoim  7179  seq3id3  10510  seq3id2  10512  seq3z  10514  fsum3cvg  11389  summodclem2a  11392  fproddccvg  11583  algfx  12055  ennnfonelemim  12428  reeff1oleme  14333  sin0pilem2  14343  bj-charfunbi  14703  nninfomnilem  14907  trilpolemlt1  14929  redcwlpolemeq1  14942  nconstwlpolem0  14951  nconstwlpolem  14953  neapmkvlem  14955
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