Theorem 2eximdv

Description: Deduction form of Theorem 19.22 of Margaris p. 90 with two quantifiers, see exim . (Contributed by NM, 3-Aug-1995)

	Ref	Expression
Hypothesis	2alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	2eximdv	⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → ∃ 𝑥 ∃ 𝑦 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		2alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	eximdv	⊢ ( 𝜑 → ( ∃ 𝑦 𝜓 → ∃ 𝑦 𝜒 ) )
3	2	eximdv	⊢ ( 𝜑 → ( ∃ 𝑥 ∃ 𝑦 𝜓 → ∃ 𝑥 ∃ 𝑦 𝜒 ) )