Theorem alrimdv

Description: Deduction form of Theorem 19.21 of Margaris p. 90. See 19.21 and 19.21v . (Contributed by NM, 10-Feb-1997)

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

Proof

Step	Hyp	Ref	Expression
1		alrimdv.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3		ax-5	⊢ ( 𝜓 → ∀ 𝑥 𝜓 )
4	2 3 1	alrimdh	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) )