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Theorem fveqeq2 5525
Description: Equality deduction for function value. (Contributed by BJ, 31-Aug-2022.)
Assertion
Ref Expression
fveqeq2  |-  ( A  =  B  ->  (
( F `  A
)  =  C  <->  ( F `  B )  =  C ) )

Proof of Theorem fveqeq2
StepHypRef Expression
1 id 19 . 2  |-  ( A  =  B  ->  A  =  B )
21fveqeq2d 5524 1  |-  ( A  =  B  ->  (
( F `  A
)  =  C  <->  ( F `  B )  =  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105    = wceq 1353   ` cfv 5217
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 2740  df-un 3134  df-sn 3599  df-pr 3600  df-op 3602  df-uni 3811  df-br 4005  df-iota 5179  df-fv 5225
This theorem is referenced by:  nnnninfeq2  7127  fodjum  7144  fodju0  7145  fodjuomnilemres  7146  fodjumkvlemres  7157  fodjumkv  7158  enmkvlem  7159  enwomnilem  7167  nninfwlporlemd  7170  nninfwlpoimlemginf  7174  nninfwlpoim  7176  seq3id3  10507  seq3id2  10509  seq3z  10511  fsum3cvg  11386  summodclem2a  11389  fproddccvg  11580  algfx  12052  ennnfonelemim  12425  reeff1oleme  14196  sin0pilem2  14206  bj-charfunbi  14566  nninfomnilem  14770  trilpolemlt1  14792  redcwlpolemeq1  14805  nconstwlpolem0  14813  nconstwlpolem  14815  neapmkvlem  14817
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