Metamath Proof Explorer

Theorem sb8v

Description: Substitution of variable in universal quantifier. Version of sb8 with a disjoint variable condition, not requiring ax-13 . (Contributed by NM, 16-May-1993) (Revised by Wolf Lammen, 19-Jan-2023)

Ref Expression
Hypothesis y φ
Assertion sb8v x φ y y x φ


Step Hyp Ref Expression
1 y φ
2 nfs1v x y x φ
3 sbequ12 x = y φ y x φ
4 1 2 3 cbvalv1 x φ y y x φ