Theorem hbabg

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 . See hbab for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by NM, 1-Mar-1995) (New usage is discouraged.)

	Ref	Expression
Hypothesis	hbabg.1	|- ( ph -> A. x ph )
Assertion	hbabg	|- ( z e. { y | ph } -> A. x z e. { y | ph } )

Proof

Step	Hyp	Ref	Expression
1		hbabg.1	|- ( ph -> A. x ph )
2		df-clab	|- ( z e. { y | ph } <-> [ z / y ] ph )
3	1	hbsb	|- ( [ z / y ] ph -> A. x [ z / y ] ph )
4	2 3	hbxfrbi	|- ( z e. { y | ph } -> A. x z e. { y | ph } )