Theorem moimi

Description: The at-most-one quantifier reverses implication. (Contributed by NM, 15-Feb-2006)

	Ref	Expression
Hypothesis	moimi.1	⊢ ( 𝜑 → 𝜓 )
Assertion	moimi	⊢ ( ∃* 𝑥 𝜓 → ∃* 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		moimi.1	⊢ ( 𝜑 → 𝜓 )
2		moim	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∃* 𝑥 𝜓 → ∃* 𝑥 𝜑 ) )
3	2 1	mpg	⊢ ( ∃* 𝑥 𝜓 → ∃* 𝑥 𝜑 )