Theorem nfsbc1d

Description: Deduction version of nfsbc1 . (Contributed by NM, 23-May-2006) (Revised by Mario Carneiro, 12-Oct-2016)

	Ref	Expression
Hypothesis	nfsbc1d.2	|- ( ph -> F/_ x A )
Assertion	nfsbc1d	|- ( ph -> F/ x [. A / x ]. ps )

Proof

Step	Hyp	Ref	Expression
1		nfsbc1d.2	|- ( ph -> F/_ x A )
2		df-sbc	|- ( [. A / x ]. ps <-> A e. { x | ps } )
3		nfab1	|- F/_ x { x | ps }
4	3	a1i	|- ( ph -> F/_ x { x | ps } )
5	1 4	nfeld	|- ( ph -> F/ x A e. { x | ps } )
6	2 5	nfxfrd	|- ( ph -> F/ x [. A / x ]. ps )