Metamath Proof Explorer


Theorem sb8

Description: Substitution of variable in universal quantifier. Usage of this theorem is discouraged because it depends on ax-13 . For a version requiring disjoint variables, but fewer axioms, see sb8v . (Contributed by NM, 16-May-1993) (Revised by Mario Carneiro, 6-Oct-2016) (Proof shortened by Jim Kingdon, 15-Jan-2018) (New usage is discouraged.)

Ref Expression
Hypothesis sb8.1 y φ
Assertion sb8 x φ y y x φ

Proof

Step Hyp Ref Expression
1 sb8.1 y φ
2 1 nfs1 x y x φ
3 sbequ12 x = y φ y x φ
4 1 2 3 cbval x φ y y x φ