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Theorem fveqeq2 5524
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 5523 1  |-  ( A  =  B  ->  (
( F `  A
)  =  C  <->  ( F `  B )  =  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 105    = wceq 1353   ` cfv 5216
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 2739  df-un 3133  df-sn 3598  df-pr 3599  df-op 3601  df-uni 3810  df-br 4004  df-iota 5178  df-fv 5224
This theorem is referenced by:  nnnninfeq2  7126  fodjum  7143  fodju0  7144  fodjuomnilemres  7145  fodjumkvlemres  7156  fodjumkv  7157  enmkvlem  7158  enwomnilem  7166  nninfwlporlemd  7169  nninfwlpoimlemginf  7173  nninfwlpoim  7175  seq3id3  10504  seq3id2  10506  seq3z  10508  fsum3cvg  11381  summodclem2a  11384  fproddccvg  11575  algfx  12046  ennnfonelemim  12419  reeff1oleme  14124  sin0pilem2  14134  bj-charfunbi  14483  nninfomnilem  14687  trilpolemlt1  14709  redcwlpolemeq1  14722  nconstwlpolem0  14730  nconstwlpolem  14732  neapmkvlem  14734
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