Theorem cosseqd

Description: Equality theorem for the classes of cosets by A and B , deduction form. (Contributed by Peter Mazsa, 4-Nov-2019)

	Ref	Expression
Hypothesis	cosseqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	cosseqd	⊢ ( 𝜑 → ≀ 𝐴 = ≀ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		cosseqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		cosseq	⊢ ( 𝐴 = 𝐵 → ≀ 𝐴 = ≀ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → ≀ 𝐴 = ≀ 𝐵 )