Theorem alrimd

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

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

Proof

Step	Hyp	Ref	Expression
1		alrimd.1	⊢ Ⅎ 𝑥 𝜑
2		alrimd.2	⊢ Ⅎ 𝑥 𝜓
3		alrimd.3	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	2	a1i	⊢ ( 𝜑 → Ⅎ 𝑥 𝜓 )
5	1 4 3	alrimdd	⊢ ( 𝜑 → ( 𝜓 → ∀ 𝑥 𝜒 ) )