Metamath Proof Explorer


Theorem sbequ6

Description: Substitution does not change a distinctor. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 5-Aug-1993) (New usage is discouraged.)

Ref Expression
Assertion sbequ6
|- ( [ w / z ] -. A. x x = y <-> -. A. x x = y )

Proof

Step Hyp Ref Expression
1 nfnae
 |-  F/ z -. A. x x = y
2 1 sbf
 |-  ( [ w / z ] -. A. x x = y <-> -. A. x x = y )