Theorem alimi

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 5-Jan-1993)

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

Proof

Step	Hyp	Ref	Expression
1		alimi.1	⊢ ( 𝜑 → 𝜓 )
2		alim	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 ) )
3	2 1	mpg	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 𝜓 )