Theorem bj-hbsb2av

Description: Version of hbsb2a with a disjoint variable condition, which does not require ax-13 . (Contributed by BJ, 11-Sep-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-hbsb2av	|- ( [ y / x ] A. y ph -> A. x [ y / x ] ph )

Proof

Step	Hyp	Ref	Expression
1		sb4av	|- ( [ y / x ] A. y ph -> A. x ( x = y -> ph ) )
2		sb6	|- ( [ y / x ] ph <-> A. x ( x = y -> ph ) )
3	2	biimpri	|- ( A. x ( x = y -> ph ) -> [ y / x ] ph )
4	3	axc4i	|- ( A. x ( x = y -> ph ) -> A. x [ y / x ] ph )
5	1 4	syl	|- ( [ y / x ] A. y ph -> A. x [ y / x ] ph )