Theorem difeq1d

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

	Ref	Expression
Hypothesis	difeq1d.1	|- ( ph -> A = B )
Assertion	difeq1d	|- ( ph -> ( A \ C ) = ( B \ C ) )

Proof

Step	Hyp	Ref	Expression
1		difeq1d.1	|- ( ph -> A = B )
2		difeq1	|- ( A = B -> ( A \ C ) = ( B \ C ) )
3	1 2	syl	|- ( ph -> ( A \ C ) = ( B \ C ) )