Theorem eceq1i

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

	Ref	Expression
Hypothesis	eceq1i.1	|- A = B
Assertion	eceq1i	|- [ A ] C = [ B ] C

Proof

Step	Hyp	Ref	Expression
1		eceq1i.1	|- A = B
2		eceq1	|- ( A = B -> [ A ] C = [ B ] C )
3	1 2	ax-mp	|- [ A ] C = [ B ] C