Theorem difeq12

Description: Equality theorem for class difference. (Contributed by FL, 31-Aug-2009)

	Ref	Expression
Assertion	difeq12	$$⊢\left(A=B\wedge C=D\right)\to A\setminus C=B\setminus D$$

Proof

Step	Hyp	Ref	Expression
1		difeq1	$$⊢A=B\to A\setminus C=B\setminus C$$
2		difeq2	$$⊢C=D\to B\setminus C=B\setminus D$$
3	1 2	sylan9eq	$$⊢\left(A=B\wedge C=D\right)\to A\setminus C=B\setminus D$$