Theorem difeq1d

Description: Deduction adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002)

	Ref	Expression
Hypothesis	difeq1d.1	$$⊢\phi \to A=B$$
Assertion	difeq1d	$$⊢\phi \to A\setminus C=B\setminus C$$

Proof

Step	Hyp	Ref	Expression
1		difeq1d.1	$$⊢\phi \to A=B$$
2		difeq1	$$⊢A=B\to A\setminus C=B\setminus C$$
3	1 2	syl	$$⊢\phi \to A\setminus C=B\setminus C$$