Theorem sbco4lem

Lemma for sbco4. It replaces the temporary variable \( v \) with another temporary variable \( w \). (Contributed by Jim Kingdon, 26-Sep-2018.) (Proof shortened by Wolf Lammen, 12-Oct-2024.) Avoid [ax-11]. (Revised by SN, 3-Sep-2025.)

Conclusion
\( \vdash [ x / v ] \, [ y / x ] \, [ v / y ] \, \varphi \leftrightarrow [ x / w ] \, [ y / x ] \, [ w / y ] \, \varphi \)
Proof
sbequ
sbbidv _
cbvsbv _