Theorem mpteq1i

Description: An equality theorem for the maps-to notation. (Contributed by Glauco Siliprandi, 17-Aug-2020)

	Ref	Expression
Hypothesis	mpteq1i.1	⊢ 𝐴 = 𝐵
Assertion	mpteq1i	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) = ( 𝑥 ∈ 𝐵 ↦ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		mpteq1i.1	⊢ 𝐴 = 𝐵
2		mpteq1	⊢ ( 𝐴 = 𝐵 → ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) = ( 𝑥 ∈ 𝐵 ↦ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) = ( 𝑥 ∈ 𝐵 ↦ 𝐶 )