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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