Metamath Proof Explorer


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 φxφ
Assertion hbabg zy|φxzy|φ

Proof

Step Hyp Ref Expression
1 hbabg.1 φxφ
2 df-clab zy|φzyφ
3 1 hbsb zyφxzyφ
4 2 3 hbxfrbi zy|φxzy|φ