Theorem fvressn 7155

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	⊢ (𝑋 ∈ 𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋))

Proof of Theorem fvressn

Step	Hyp	Ref	Expression
1		snidg 4657	. 2 ⊢ (𝑋 ∈ 𝑉 → 𝑋 ∈ {𝑋})
2	1	fvresd 6904	1 ⊢ (𝑋 ∈ 𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋))

Syntax hints:   → wi 4   = wceq 1533   ∈ wcel 2098  {csn 4623   ↾ cres 5671  ‘cfv 6536

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ral 3056  df-rex 3065  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-opab 5204  df-xp 5675  df-res 5681  df-iota 6488  df-fv 6544

This theorem is referenced by:  fvn0fvelrnOLD  7156  fvunsn  7172  funressndmfvrn  46308