This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem eceq1d

Description: Equality theorem for equivalence class (deduction form). (Contributed by Jim Kingdon, 31-Dec-2019)

		Ref	Expression
	Hypothesis	eceq1d.1	$⊢ φ \to A = B$
	Assertion	eceq1d	$⊢ φ \to [A] C = [B] C$

Step	Hyp	Ref	Expression
1		eceq1d.1	$⊢ φ \to A = B$
2		eceq1	$⊢ A = B \to [A] C = [B] C$
3	1 2	syl	$⊢ φ \to [A] C = [B] C$