Theorem hblemg

Description: Change the free variable of a hypothesis builder. Usage of this theorem is discouraged because it depends on ax-13 . See hblem for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by NM, 21-Jun-1993) (Revised by Andrew Salmon, 11-Jul-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	hblemg.1	|- ( y e. A -> A. x y e. A )
Assertion	hblemg	|- ( z e. A -> A. x z e. A )

Proof

Step	Hyp	Ref	Expression
1		hblemg.1	|- ( y e. A -> A. x y e. A )
2	1	hbsb	|- ( [ z / y ] y e. A -> A. x [ z / y ] y e. A )
3		clelsb1	|- ( [ z / y ] y e. A <-> z e. A )
4	3	albii	|- ( A. x [ z / y ] y e. A <-> A. x z e. A )
5	2 3 4	3imtr3i	|- ( z e. A -> A. x z e. A )