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	$$⊢\left[C\right]A=\left[C\right]B$$

Proof

Step	Hyp	Ref	Expression
1		eceq2i.1	$$⊢A=B$$
2		eceq2	$$⊢A=B\to \left[C\right]A=\left[C\right]B$$
3	1 2	ax-mp	$$⊢\left[C\right]A=\left[C\right]B$$