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 )