Theorem eceq2d

Description: Equality theorem for the A -coset and B -coset of C , deduction version. (Contributed by Peter Mazsa, 23-Apr-2021)

	Ref	Expression
Hypothesis	eceq2d.1	|- ( ph -> A = B )
Assertion	eceq2d	|- ( ph -> [ C ] A = [ C ] B )

Proof

Step	Hyp	Ref	Expression
1		eceq2d.1	|- ( ph -> A = B )
2		eceq2	|- ( A = B -> [ C ] A = [ C ] B )
3	1 2	syl	|- ( ph -> [ C ] A = [ C ] B )