Theorem fvressn 7181

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 4664	. 2 ⊢ (𝑋 ∈ 𝑉 → 𝑋 ∈ {𝑋})
2	1	fvresd 6926	1 ⊢ (𝑋 ∈ 𝑉 → ((𝐹 ↾ {𝑋})‘𝑋) = (𝐹‘𝑋))

Syntax hints:   → wi 4   = wceq 1536   ∈ wcel 2105  {csn 4630   ↾ cres 5690  ‘cfv 6562

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-sep 5301  ax-nul 5311  ax-pr 5437

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3059  df-rex 3068  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-in 3969  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-opab 5210  df-xp 5694  df-res 5700  df-iota 6515  df-fv 6570

This theorem is referenced by:  fvn0fvelrnOLD  7182  fvunsn  7198  funressndmfvrn  46993