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	⊢ Ⅎ 𝑥 𝐴
Assertion	nfsbc1	⊢ Ⅎ 𝑥 [ 𝐴 / 𝑥 ] 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfsbc1.1	⊢ Ⅎ 𝑥 𝐴
2	1	a1i	⊢ ( ⊤ → Ⅎ 𝑥 𝐴 )
3	2	nfsbc1d	⊢ ( ⊤ → Ⅎ 𝑥 [ 𝐴 / 𝑥 ] 𝜑 )
4	3	mptru	⊢ Ⅎ 𝑥 [ 𝐴 / 𝑥 ] 𝜑