Theorem eceq1

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

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

Proof

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