Theorem nfsbc1

Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993) (Revised by Mario Carneiro, 12-Oct-2016)

	Ref	Expression
Hypothesis	nfsbc1.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	nfsbc1	$$⊢Ⅎx\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfsbc1.1	$$⊢\underset{\_}{Ⅎ}xA$$
2	1	a1i	$$⊢\top \to \underset{\_}{Ⅎ}xA$$
3	2	nfsbc1d	$$⊢\top \to Ⅎx\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi$$
4	3	mptru	$$⊢Ⅎx\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi$$