Theorem cosseqi

Description: Equality theorem for the classes of cosets by A and B , inference form. (Contributed by Peter Mazsa, 9-Jan-2018)

	Ref	Expression
Hypothesis	cosseqi.1	|- A = B
Assertion	cosseqi	|- ,~ A = ,~ B

Proof

Step	Hyp	Ref	Expression
1		cosseqi.1	|- A = B
2		cosseq	|- ( A = B -> ,~ A = ,~ B )
3	1 2	ax-mp	|- ,~ A = ,~ B