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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 )