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