Theorem eceq2

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

	Ref	Expression
Assertion	eceq2	$$⊢A=B\to \left[C\right]A=\left[C\right]B$$

Proof

Step	Hyp	Ref	Expression
1		imaeq1	$$⊢A=B\to A\left[\left\{C\right\}\right]=B\left[\left\{C\right\}\right]$$
2		df-ec	$$⊢\left[C\right]A=A\left[\left\{C\right\}\right]$$
3		df-ec	$$⊢\left[C\right]B=B\left[\left\{C\right\}\right]$$
4	1 2 3	3eqtr4g	$$⊢A=B\to \left[C\right]A=\left[C\right]B$$