Theorem dfin5

Description: Alternate definition for the intersection of two classes. (Contributed by NM, 6-Jul-2005)

	Ref	Expression
Assertion	dfin5	$$⊢A\cap B=\left\{x\in A|x\in B\right\}$$

Proof

Step	Hyp	Ref	Expression
1		df-in	$$⊢A\cap B=\left\{x|\left(x\in A\wedge x\in B\right)\right\}$$
2		df-rab	$$⊢\left\{x\in A|x\in B\right\}=\left\{x|\left(x\in A\wedge x\in B\right)\right\}$$
3	1 2	eqtr4i	$$⊢A\cap B=\left\{x\in A|x\in B\right\}$$