Theorem ralrimiva

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 2-Jan-2006)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimiva.1	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝜓 )
2	1	ex	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 → 𝜓 ) )
3	2	ralrimiv	⊢ ( 𝜑 → ∀ 𝑥 ∈ 𝐴 𝜓 )