Theorem exlimdh

Description: Deduction form of Theorem 19.9 of Margaris p. 89. (Contributed by NM, 28-Jan-1997)

	Ref	Expression
Hypotheses	exlimdh.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
	exlimdh.2	⊢ ( 𝜒 → ∀ 𝑥 𝜒 )
	exlimdh.3	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	exlimdh	⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		exlimdh.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2		exlimdh.2	⊢ ( 𝜒 → ∀ 𝑥 𝜒 )
3		exlimdh.3	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	1	nf5i	⊢ Ⅎ 𝑥 𝜑
5	2	nf5i	⊢ Ⅎ 𝑥 𝜒
6	4 5 3	exlimd	⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → 𝜒 ) )