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Theorem fveqeq2 5396
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 5395 1  |-  ( A  =  B  ->  (
( F `  A
)  =  C  <->  ( F `  B )  =  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1314   ` cfv 5091
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-op 3504  df-uni 3705  df-br 3898  df-iota 5056  df-fv 5099
This theorem is referenced by:  fodjum  6984  fodju0  6985  fodjuomnilemres  6986  fodjumkvlemres  6999  fodjumkv  7000  seq3id3  10231  seq3id2  10233  seq3z  10235  fsum3cvg  11097  summodclem2a  11101  algfx  11640  ennnfonelemim  11843  trilpolemlt1  13068
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