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) (Revised by BJ, 29-Mar-2021)

Ref Expression
Assertion moa1 ( ∃* 𝑥 ( 𝜑𝜓 ) → ∃* 𝑥 𝜓 )

Proof

Step Hyp Ref Expression
1 ax-1 ( 𝜓 → ( 𝜑𝜓 ) )
2 1 moimi ( ∃* 𝑥 ( 𝜑𝜓 ) → ∃* 𝑥 𝜓 )