Metamath Proof Explorer

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	$⊢ [C] A = [C] B$

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