Theorem fvmpt4

Description: Value of a function given by the maps-to notation. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Assertion	fvmpt4	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝐵 ∈ 𝐶 ) → ( ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ‘ 𝑥 ) = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐵 )
2	1	fvmpt2	⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝐵 ∈ 𝐶 ) → ( ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) ‘ 𝑥 ) = 𝐵 )