Theorem difeq12d

Description: Equality deduction for class difference. (Contributed by FL, 29-May-2014)

	Ref	Expression
Hypotheses	difeq12d.1	$$⊢\phi \to A=B$$
	difeq12d.2	$$⊢\phi \to C=D$$
Assertion	difeq12d	$$⊢\phi \to A\setminus C=B\setminus D$$

Proof

Step	Hyp	Ref	Expression
1		difeq12d.1	$$⊢\phi \to A=B$$
2		difeq12d.2	$$⊢\phi \to C=D$$
3	1	difeq1d	$$⊢\phi \to A\setminus C=B\setminus C$$
4	2	difeq2d	$$⊢\phi \to B\setminus C=B\setminus D$$
5	3 4	eqtrd	$$⊢\phi \to A\setminus C=B\setminus D$$