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Theorem fvresd 6369
Description: The value of a restricted function, deduction version of fvres 6368. (Contributed by Glauco Siliprandi, 8-Apr-2021.)
Hypothesis
Ref Expression
fvresd.1 (𝜑𝐴𝐵)
Assertion
Ref Expression
fvresd (𝜑 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))

Proof of Theorem fvresd
StepHypRef Expression
1 fvresd.1 . 2 (𝜑𝐴𝐵)
2 fvres 6368 . 2 (𝐴𝐵 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))
31, 2syl 17 1 (𝜑 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1632  wcel 2139  cres 5268  cfv 6049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ral 3055  df-rex 3056  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-sn 4322  df-pr 4324  df-op 4328  df-uni 4589  df-br 4805  df-opab 4865  df-xp 5272  df-res 5278  df-iota 6012  df-fv 6057
This theorem is referenced by:  ackbij2lem2  9254  cfsmolem  9284  txkgen  21657  loglesqrt  24698  uhgrspansubgrlem  26381  wlkres  26777  ftc2re  30985  reprsuc  31002  frrlem4  32089  nolesgn2o  32130  nolesgn2ores  32131  noresle  32152  noprefixmo  32154  nosupres  32159  nosupbnd2lem1  32167  noetalem3  32171  limsupresxr  40501  liminfresxr  40502  sssmf  41453
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