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Theorem fvresd 6118
 Description: The value of a restricted function, deduction version of fvres 6117. (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 6117 . 2 (𝐴𝐵 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))
31, 2syl 17 1 (𝜑 → ((𝐹𝐵)‘𝐴) = (𝐹𝐴))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∈ wcel 1977   ↾ cres 5040  ‘cfv 5804 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-xp 5044  df-res 5050  df-iota 5768  df-fv 5812 This theorem is referenced by:  ackbij2lem2  8945  cfsmolem  8975  txkgen  21265  loglesqrt  24299  vonval2  39559  sssmf  39625  1wlkres  40879
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