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Theorem 2fveq3 5394
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 5389 . 2  |-  ( A  =  B  ->  ( G `  A )  =  ( G `  B ) )
21fveq2d 5393 1  |-  ( A  =  B  ->  ( F `  ( G `  A ) )  =  ( F `  ( G `  B )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316   ` cfv 5093
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101
This theorem is referenced by:  difinfsnlem  6952  ctssdclemn0  6963  seq3f1olemqsum  10241  seq3f1oleml  10244  seq3f1o  10245  seq3homo  10251  seq3coll  10553  fsumf1o  11127  iserabs  11212  explecnv  11242  cvgratnnlemnexp  11261  cvgratnnlemmn  11262  alginv  11655  algcvg  11656  algcvga  11659  ctiunctlemu1st  11874  ctiunctlemu2nd  11875  ctiunctlemudc  11877  ctiunctlemfo  11879  subctctexmid  13123
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