Theorem nfcsb1d

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

	Ref	Expression
Hypothesis	nfcsb1d.1	|- ( ph -> F/_ x A )
Assertion	nfcsb1d	|- ( ph -> F/_ x [_ A / x ]_ B )

Proof

Step	Hyp	Ref	Expression
1		nfcsb1d.1	|- ( ph -> F/_ x A )
2		df-csb	|- [_ A / x ]_ B = { y | [. A / x ]. y e. B }
3		nfv	|- F/ y ph
4	1	nfsbc1d	|- ( ph -> F/ x [. A / x ]. y e. B )
5	3 4	nfabdw	|- ( ph -> F/_ x { y | [. A / x ]. y e. B } )
6	2 5	nfcxfrd	|- ( ph -> F/_ x [_ A / x ]_ B )