Theorem difeq2d

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

	Ref	Expression
Hypothesis	difeq1d.1	$$⊢\phi \to A=B$$
Assertion	difeq2d	$$⊢\phi \to C\setminus A=C\setminus B$$

Proof

Step	Hyp	Ref	Expression
1		difeq1d.1	$$⊢\phi \to A=B$$
2		difeq2	$$⊢A=B\to C\setminus A=C\setminus B$$
3	1 2	syl	$$⊢\phi \to C\setminus A=C\setminus B$$