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Theorem fveqeq2d 5383
Description: Equality deduction for function value. (Contributed by BJ, 30-Aug-2022.)
Hypothesis
Ref Expression
fveqeq2d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
fveqeq2d  |-  ( ph  ->  ( ( F `  A )  =  C  <-> 
( F `  B
)  =  C ) )

Proof of Theorem fveqeq2d
StepHypRef Expression
1 fveqeq2d.1 . . 3  |-  ( ph  ->  A  =  B )
21fveq2d 5379 . 2  |-  ( ph  ->  ( F `  A
)  =  ( F `
 B ) )
32eqeq1d 2123 1  |-  ( ph  ->  ( ( F `  A )  =  C  <-> 
( F `  B
)  =  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1314   ` cfv 5081
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 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 2244  df-rex 2396  df-v 2659  df-un 3041  df-sn 3499  df-pr 3500  df-op 3502  df-uni 3703  df-br 3896  df-iota 5046  df-fv 5089
This theorem is referenced by:  fveqeq2  5384  algcvga  11578
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