Theorem 19.42vv

Version of 19.42 with two quantifiers and a disjoint variable condition requiring fewer axioms. (Contributed by NM, 16-Mar-1995.)

Conclusion
\( \vdash \exists x \, \exists y \, (\varphi \wedge \psi) \leftrightarrow \varphi \wedge \exists x \, \exists y \, \psi \)
Proof
l0
exdistr
\( \vdash \exists x \, \exists y \, (\varphi \wedge \psi) \leftrightarrow \exists x \, (\varphi \wedge \exists y \, \psi) \)
19.42v
\( \vdash \exists x \, (\varphi \wedge \exists y \, \psi) \leftrightarrow \varphi \wedge \exists x \, \exists y \, \psi \)
bitri l0 _