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Theorem fvressn 6311
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 4152 . 2 (𝑋𝑉𝑋 ∈ {𝑋})
2 fvres 6101 . 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 1474  wcel 1976  {csn 4124  cres 5029  cfv 5789
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4711  ax-pr 4827
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rex 2901  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-br 4578  df-opab 4638  df-xp 5033  df-res 5039  df-iota 5753  df-fv 5797
This theorem is referenced by:  fvn0fvelrn  6312  fvunsn  6327
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