Theorem fveqeq2 5438

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

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( A = B -> A = B )
2	1	fveqeq2d 5437	1 |- ( A = B -> ( ( F ` A ) = C <-> ( F ` B ) = C ) )

Syntax hints:   -> wi 4   <-> wb 104   = wceq 1332   ` cfv 5131

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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-un 3080  df-sn 3538  df-pr 3539  df-op 3541  df-uni 3745  df-br 3938  df-iota 5096  df-fv 5139

This theorem is referenced by:  fodjum  7026  fodju0  7027  fodjuomnilemres  7028  fodjumkvlemres  7041  fodjumkv  7042  enmkvlem  7043  enwomnilem  7050  seq3id3  10311  seq3id2  10313  seq3z  10315  fsum3cvg  11179  summodclem2a  11182  fproddccvg  11373  algfx  11769  ennnfonelemim  11973  reeff1oleme  12901  sin0pilem2  12911  trilpolemlt1  13409  redcwlpolemeq1  13421  neapmkvlem  13424