Theorem csbid

Description: Analogue of sbid for proper substitution into a class. (Contributed by NM, 10-Nov-2005)

	Ref	Expression
Assertion	csbid	$$⊢⦋x/x⦌A=A$$

Proof

Step	Hyp	Ref	Expression
1		df-csb	$$⊢⦋x/x⦌A=\left\{y|\underset{\dot{}}{[}x/x\underset{\dot{}}{]}y\in A\right\}$$
2		sbcid	$$⊢\underset{\dot{}}{[}x/x\underset{\dot{}}{]}y\in A\leftrightarrow y\in A$$
3	2	abbii	$$⊢\left\{y|\underset{\dot{}}{[}x/x\underset{\dot{}}{]}y\in A\right\}=\left\{y|y\in A\right\}$$
4		abid2	$$⊢\left\{y|y\in A\right\}=A$$
5	1 3 4	3eqtri	$$⊢⦋x/x⦌A=A$$