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 ( 𝜑 → 𝜓 ) → ∃* 𝑥 𝜓 )

Proof

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