Theorem al2imi

Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 10-Jan-1993)

	Ref	Expression
Hypothesis	al2imi.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	al2imi	⊢ ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		al2imi.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		al2im	⊢ ( ∀ 𝑥 ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) ) )
3	2 1	mpg	⊢ ( ∀ 𝑥 𝜑 → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )