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 ) )