Theorem ralimi

Description: Inference quantifying both antecedent and consequent, with strong hypothesis. (Contributed by NM, 4-Mar-1997)

	Ref	Expression
Hypothesis	ralimi.1	⊢ ( 𝜑 → 𝜓 )
Assertion	ralimi	⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ralimi.1	⊢ ( 𝜑 → 𝜓 )
2	1	a1i	⊢ ( 𝑥 ∈ 𝐴 → ( 𝜑 → 𝜓 ) )
3	2	ralimia	⊢ ( ∀ 𝑥 ∈ 𝐴 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )