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