Theorem rabidim1

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

	Ref	Expression
Assertion	rabidim1	$$⊢x\in \left\{x\in A|\phi \right\}\to x\in A$$

Proof

Step	Hyp	Ref	Expression
1		rabid	$$⊢x\in \left\{x\in A|\phi \right\}\leftrightarrow \left(x\in A\wedge \phi \right)$$
2	1	simplbi	$$⊢x\in \left\{x\in A|\phi \right\}\to x\in A$$