Theorem bj-hbsb3v

Description: Version of hbsb3 with a disjoint variable condition, which does not require ax-13 . (Remark: the unbundled version of nfs1 is given by bj-nfs1v .) (Contributed by BJ, 11-Sep-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-hbsb3v.1	|- ( ph -> A. y ph )
Assertion	bj-hbsb3v	|- ( [ y / x ] ph -> A. x [ y / x ] ph )

Proof

Step	Hyp	Ref	Expression
1		bj-hbsb3v.1	|- ( ph -> A. y ph )
2	1	sbimi	|- ( [ y / x ] ph -> [ y / x ] A. y ph )
3		bj-hbsb2av	|- ( [ y / x ] A. y ph -> A. x [ y / x ] ph )
4	2 3	syl	|- ( [ y / x ] ph -> A. x [ y / x ] ph )