Metamath Proof Explorer


Theorem rspa

Description: Restricted specialization. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Assertion rspa ⊢ ∀ x ∈ A φ ∧ x ∈ A → φ

Proof

Step Hyp Ref Expression
1 rsp ⊢ ∀ x ∈ A φ → x ∈ A → φ
2 1 imp ⊢ ∀ x ∈ A φ ∧ x ∈ A → φ