Theorem difeq12d

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

	Ref	Expression
Hypotheses	difeq12d.1	|- ( ph -> A = B )
	difeq12d.2	|- ( ph -> C = D )
Assertion	difeq12d	|- ( ph -> ( A \ C ) = ( B \ D ) )

Proof

Step	Hyp	Ref	Expression
1		difeq12d.1	|- ( ph -> A = B )
2		difeq12d.2	|- ( ph -> C = D )
3	1	difeq1d	|- ( ph -> ( A \ C ) = ( B \ C ) )
4	2	difeq2d	|- ( ph -> ( B \ C ) = ( B \ D ) )
5	3 4	eqtrd	|- ( ph -> ( A \ C ) = ( B \ D ) )