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Metamath Proof Explorer

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 )