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Theorem fvressn 6571
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 4343 . 2 (𝑋𝑉𝑋 ∈ {𝑋})
2 fvres 6348 . 2 (𝑋 ∈ {𝑋} → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹𝑋))
31, 2syl 17 1 (𝑋𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹𝑋))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1630  wcel 2144  {csn 4314  cres 5251  cfv 6031
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-nul 4920  ax-pr 5034
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-uni 4573  df-br 4785  df-opab 4845  df-xp 5255  df-res 5261  df-iota 5994  df-fv 6039
This theorem is referenced by:  fvn0fvelrn  6572  fvunsn  6588
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