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Metamath Proof Explorer

Theorem moa1

Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 and exa1 . (Contributed by NM, 28-Jul-1995) (Proof shortened by Wolf Lammen, 22-Dec-2018)

Ref Expression
Assertion moa1 ⊢ ∃* x φ → ψ → ∃* x ψ

Proof

Step Hyp Ref Expression
1 ax-1 ⊢ ψ → φ → ψ
2 1 moimi ⊢ ∃* x φ → ψ → ∃* x ψ