Theorem 19.31v

Version of 19.31 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.)

Conclusion
\( \vdash \forall x \, (\varphi \vee \psi) \leftrightarrow \forall x \, \varphi \vee \psi \)
Proof
l0
19.32v
\( \vdash \forall x \, (\psi \vee \varphi) \leftrightarrow \psi \vee \forall x \, \varphi \)
orcom
l2
albii _
\( \vdash \forall x \, (\varphi \vee \psi) \leftrightarrow \forall x \, (\psi \vee \varphi) \)
orcom
\( \vdash \forall x \, \varphi \vee \psi \leftrightarrow \psi \vee \forall x \, \varphi \)
3bitr4i l0 l2 _