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Metamath Proof Explorer

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	$⊢ [A] C = [B] C$

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