Theorem alimdv

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . See alimdh and alimd for versions without a distinct variable condition. (Contributed by NM, 3-Apr-1994)

	Ref	Expression
Hypothesis	alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	alimdv	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		alimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	2 1	alimdh	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )