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Theorem 2fveq3 5426
Description: Equality theorem for nested function values. (Contributed by AV, 14-Aug-2022.)
Assertion
Ref Expression
2fveq3  |-  ( A  =  B  ->  ( F `  ( G `  A ) )  =  ( F `  ( G `  B )
) )

Proof of Theorem 2fveq3
StepHypRef Expression
1 fveq2 5421 . 2  |-  ( A  =  B  ->  ( G `  A )  =  ( G `  B ) )
21fveq2d 5425 1  |-  ( A  =  B  ->  ( F `  ( G `  A ) )  =  ( F `  ( G `  B )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331   ` cfv 5123
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131
This theorem is referenced by:  difinfsnlem  6984  ctssdclemn0  6995  cc2  7082  seq3f1olemqsum  10280  seq3f1oleml  10283  seq3f1o  10284  seq3homo  10290  seq3coll  10592  fsumf1o  11166  iserabs  11251  explecnv  11281  cvgratnnlemnexp  11300  cvgratnnlemmn  11301  alginv  11735  algcvg  11736  algcvga  11739  ctiunctlemu1st  11954  ctiunctlemu2nd  11955  ctiunctlemudc  11957  ctiunctlemfo  11959  subctctexmid  13226
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