Metamath Proof Explorer


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 yAxyA
Assertion hblemg zAxzA

Proof

Step Hyp Ref Expression
1 hblemg.1 yAxyA
2 1 hbsb zyyAxzyyA
3 clelsb1 zyyAzA
4 3 albii xzyyAxzA
5 2 3 4 3imtr3i zAxzA