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