Theorem eceq2i

Description: Equality theorem for the A -coset and B -coset of C , inference version. (Contributed by Peter Mazsa, 11-May-2021)

	Ref	Expression
Hypothesis	eceq2i.1	|- A = B
Assertion	eceq2i	|- [ C ] A = [ C ] B

Proof

Step	Hyp	Ref	Expression
1		eceq2i.1	|- A = B
2		eceq2	|- ( A = B -> [ C ] A = [ C ] B )
3	1 2	ax-mp	|- [ C ] A = [ C ] B