Theorem mpteq2dv

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 23-Aug-2014)

	Ref	Expression
Hypothesis	mpteq2dv.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	mpteq2dv	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) )

Proof

Step	Hyp	Ref	Expression
1		mpteq2dv.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝐵 = 𝐶 )
3	2	mpteq2dva	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐴 ↦ 𝐶 ) )