Theorem exlimdv

Description: Deduction form of Theorem 19.23 of Margaris p. 90, see 19.23 . (Contributed by NM, 27-Apr-1994) Remove dependencies on ax-6 , ax-7 . (Revised by Wolf Lammen, 4-Dec-2017)

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

Proof

Step	Hyp	Ref	Expression
1		exlimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	eximdv	⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 ) )
3		ax5e	⊢ ( ∃ 𝑥 𝜒 → 𝜒 )
4	2 3	syl6	⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → 𝜒 ) )