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Metamath Proof Explorer

Theorem eceq2d

Description: Equality theorem for the A -coset and B -coset of C , deduction version. (Contributed by Peter Mazsa, 23-Apr-2021)

		Ref	Expression
	Hypothesis	eceq2d.1	$⊢ φ \to A = B$
	Assertion	eceq2d	$⊢ φ \to [C] A = [C] B$

Step	Hyp	Ref	Expression
1		eceq2d.1	$⊢ φ \to A = B$
2		eceq2	$⊢ A = B \to [C] A = [C] B$
3	1 2	syl	$⊢ φ \to [C] A = [C] B$