Theorem hbsb2

Description: Bound-variable hypothesis builder for substitution. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 14-May-1993) (New usage is discouraged.)

	Ref	Expression
Assertion	hbsb2	|- ( -. A. x x = y -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )

Proof

Step	Hyp	Ref	Expression
1		sb4b	|- ( -. A. x x = y -> ( [ y / x ] ph <-> A. x ( x = y -> ph ) ) )
2		sb2	|- ( A. x ( x = y -> ph ) -> [ y / x ] ph )
3	2	axc4i	|- ( A. x ( x = y -> ph ) -> A. x [ y / x ] ph )
4	1 3	syl6bi	|- ( -. A. x x = y -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )