Theorem alrimdd

Description: Deduction form of Theorem 19.21 of Margaris p. 90, see 19.21 . (Contributed by Mario Carneiro, 24-Sep-2016)

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

Proof

Step	Hyp	Ref	Expression
1		alrimdd.1	⊢ Ⅎ 𝑥 𝜑
2		alrimdd.2	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
3		alrimdd.3	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	2	nf5rd	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜓 ) )
5	1 3	alimd	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )
6	4 5	syld	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) )