Theorem dfdif2

Description: Alternate definition of class difference. (Contributed by NM, 25-Mar-2004)

	Ref	Expression
Assertion	dfdif2	$$⊢A\setminus B=\left\{x\in A|\neg x\in B\right\}$$

Proof

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