Theorem moimdv

Description: The at-most-one quantifier reverses implication, deduction form. (Contributed by Thierry Arnoux, 25-Feb-2017)

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

Proof

Step	Hyp	Ref	Expression
1		moimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	alrimiv	⊢ ( 𝜑 → ∀ 𝑥 ( 𝜓 → 𝜒 ) )
3		moim	⊢ ( ∀ 𝑥 ( 𝜓 → 𝜒 ) → ( ∃* 𝑥 𝜒 → ∃* 𝑥 𝜓 ) )
4	2 3	syl	⊢ ( 𝜑 → ( ∃* 𝑥 𝜒 → ∃* 𝑥 𝜓 ) )