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Metamath Proof Explorer

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 ) )