ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fvresd GIF version

Theorem fvresd 5519
Description: The value of a restricted function, deduction version of fvres 5518. (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 5518 . 2 (𝐴𝐵 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))
31, 2syl 14 1 (𝜑 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  wcel 2141  cres 4611  cfv 5196
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-14 2144  ax-ext 2152  ax-sep 4105  ax-pow 4158  ax-pr 4192
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rex 2454  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-pw 3566  df-sn 3587  df-pr 3588  df-op 3590  df-uni 3795  df-br 3988  df-opab 4049  df-xp 4615  df-res 4621  df-iota 5158  df-fv 5204
This theorem is referenced by:  difinfsn  7074  upxp  13027  uptx  13029  reeflog  13539  relogef  13540  trilpolemlt1  14035
  Copyright terms: Public domain W3C validator