Theorem nfcsb1d

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016)

	Ref	Expression
Hypothesis	nfcsb1d.1	$$⊢\phi \to \underset{\_}{Ⅎ}xA$$
Assertion	nfcsb1d	$$⊢\phi \to \underset{\_}{Ⅎ}x⦋A/x⦌B$$

Proof

Step	Hyp	Ref	Expression
1		nfcsb1d.1	$$⊢\phi \to \underset{\_}{Ⅎ}xA$$
2		df-csb	$$⊢⦋A/x⦌B=\left\{y|\underset{\dot{}}{[}A/x\underset{\dot{}}{]}y\in B\right\}$$
3		nfv	$$⊢Ⅎy\phi$$
4	1	nfsbc1d	$$⊢\phi \to Ⅎx\underset{\dot{}}{[}A/x\underset{\dot{}}{]}y\in B$$
5	3 4	nfabdw	$$⊢\phi \to \underset{\_}{Ⅎ}x\left\{y|\underset{\dot{}}{[}A/x\underset{\dot{}}{]}y\in B\right\}$$
6	2 5	nfcxfrd	$$⊢\phi \to \underset{\_}{Ⅎ}x⦋A/x⦌B$$