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	$$⊢\left[A\right]C=\left[B\right]C$$

Proof

Step	Hyp	Ref	Expression
1		eceq1i.1	$$⊢A=B$$
2		eceq1	$$⊢A=B\to \left[A\right]C=\left[B\right]C$$
3	1 2	ax-mp	$$⊢\left[A\right]C=\left[B\right]C$$