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Metamath Proof Explorer

Theorem eceq1

Description: Equality theorem for equivalence class. (Contributed by NM, 23-Jul-1995)

		Ref	Expression
	Assertion	eceq1	$⊢ A = B \to [A] C = [B] C$

Step	Hyp	Ref	Expression
1		sneq	$⊢ A = B \to \{A\} = \{B\}$
2	1	imaeq2d	$⊢ A = B \to C [\{A\}] = C [\{B\}]$
3		df-ec	$⊢ [A] C = C [\{A\}]$
4		df-ec	$⊢ [B] C = C [\{B\}]$
5	2 3 4	3eqtr4g	$⊢ A = B \to [A] C = [B] C$