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Metamath Proof Explorer

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 )