Metamath Proof Explorer


Theorem rabidim1

Description: Membership in a restricted abstraction, implication. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Assertion rabidim1 ⊢ x ∈ x ∈ A | φ → x ∈ A

Proof

Step Hyp Ref Expression
1 rabid ⊢ x ∈ x ∈ A | φ ↔ x ∈ A ∧ φ
2 1 simplbi ⊢ x ∈ x ∈ A | φ → x ∈ A