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Metamath Proof Explorer

Theorem mpteq2dva

Description: Slightly more general equality inference for the maps-to notation. (Contributed by Scott Fenton, 25-Apr-2012) Remove dependency on ax-10 . (Revised by SN, 11-Nov-2024)

Ref Expression
Hypothesis mpteq2dva.1 ⊢ φ ∧ x ∈ A → B = C
Assertion mpteq2dva ⊢ φ → x ∈ A ⟼ B = x ∈ A ⟼ C

Proof

Step Hyp Ref Expression
1 mpteq2dva.1 ⊢ φ ∧ x ∈ A → B = C
2 eqidd ⊢ φ → A = A
3 2 1 mpteq12dva ⊢ φ → x ∈ A ⟼ B = x ∈ A ⟼ C