Theorem mpteq2i

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013)

	Ref	Expression
Hypothesis	mpteq2i.1	⊢ 𝐵 = 𝐶
Assertion	mpteq2i	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		mpteq2i.1	⊢ 𝐵 = 𝐶
2	1	a1i	⊢ ( 𝑥 ∈ 𝐴 → 𝐵 = 𝐶 )
3	2	mpteq2ia	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐶 )