Metamath Proof Explorer


Theorem sbcov

Description: A composition law for substitution. Version of sbco with a disjoint variable condition using fewer axioms. (Contributed by NM, 14-May-1993) (Revised by GG, 7-Aug-2023) (Proof shortened by SN, 26-Aug-2025)

Ref Expression
Assertion sbcov y x x y φ y x φ

Proof

Step Hyp Ref Expression
1 sbequ12r x = y x y φ φ
2 1 sbbiiev y x x y φ y x φ