Theorem sbcov

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.)

Conclusion
\( \vdash [ y / x ] \, [ x / y ] \, \varphi \leftrightarrow [ y / x ] \, \varphi \)
Proof
sbequ12r
sbbiiev _