Theorem 19.42v

Version of 19.42 with a disjoint variable condition requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)

Conclusion
\( \vdash \exists x \, (\varphi \wedge \psi) \leftrightarrow \varphi \wedge \exists x \, \psi \)
Proof
l0
19.41v
\( \vdash \exists x \, (\psi \wedge \varphi) \leftrightarrow \exists x \, \psi \wedge \varphi \)
l1
exancom
\( \vdash \exists x \, (\varphi \wedge \psi) \leftrightarrow \exists x \, (\psi \wedge \varphi) \)
ancom
\( \vdash \varphi \wedge \exists x \, \psi \leftrightarrow \exists x \, \psi \wedge \varphi \)
3bitr4i l0 l1 _