Theorem rabid

Description: An "identity" law of concretion for restricted abstraction. Special case of Definition 2.1 of Quine p. 16. (Contributed by NM, 9-Oct-2003)

	Ref	Expression
Assertion	rabid	$$⊢x\in \left\{x\in A|\phi \right\}\leftrightarrow \left(x\in A\wedge \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-rab	$$⊢\left\{x\in A|\phi \right\}=\left\{x|\left(x\in A\wedge \phi \right)\right\}$$
2	1	abeq2i	$$⊢x\in \left\{x\in A|\phi \right\}\leftrightarrow \left(x\in A\wedge \phi \right)$$