This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem fvressn

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)

		Ref	Expression
	Assertion	fvressn	⊢ ( 𝑋 ∈ 𝑉 → ( ( 𝐹 ↾ { 𝑋 } ) ‘ 𝑋 ) = ( 𝐹 ‘ 𝑋 ) )

Proof

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