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Theorem fvressn 7171
Description: The value of a function restricted to the singleton containing the argument equals the value of the function for this argument. (Contributed by Alexander van der Vekens, 22-Jul-2018.)
Assertion
Ref Expression
fvressn (𝑋𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹𝑋))

Proof of Theorem fvressn
StepHypRef Expression
1 snidg 4663 . 2 (𝑋𝑉𝑋 ∈ {𝑋})
21fvresd 6917 1 (𝑋𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹𝑋))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1534  wcel 2099  {csn 4629  cres 5680  cfv 6548
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4909  df-br 5149  df-opab 5211  df-xp 5684  df-res 5690  df-iota 6500  df-fv 6556
This theorem is referenced by:  fvn0fvelrnOLD  7172  fvunsn  7188  funressndmfvrn  46426
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