Theorem 19.45v

Version of 19.45 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 12-Mar-1993.)

Conclusion
\( \vdash \exists x \, (\varphi \vee \psi) \leftrightarrow \varphi \vee \exists x \, \psi \)
Proof
l0
19.43
\( \vdash \exists x \, (\varphi \vee \psi) \leftrightarrow \exists x \, \varphi \vee \exists x \, \psi \)
19.9v
orbi1i _
\( \vdash \exists x \, \varphi \vee \exists x \, \psi \leftrightarrow \varphi \vee \exists x \, \psi \)
bitri l0 _