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Metamath Proof Explorer

Theorem rgenw

Description: Generalization rule for restricted quantification. (Contributed by NM, 18-Jun-2014)

Ref Expression
Hypothesis rgenw.1 ⊢ 𝜑
Assertion rgenw ∀ 𝑥 ∈ 𝐴 𝜑

Proof

Step Hyp Ref Expression
1 rgenw.1 ⊢ 𝜑
2 1 a1i ⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )
3 2 rgen ⊢ ∀ 𝑥 ∈ 𝐴 𝜑