Theorem 19.37v

Version of 19.37 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)

Conclusion
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \varphi \rightarrow \exists x \, \psi \)
Proof
l0
19.35
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, \varphi \rightarrow \exists x \, \psi \)
19.3v
imbi1i _
\( \vdash \forall x \, \varphi \rightarrow \exists x \, \psi \leftrightarrow \varphi \rightarrow \exists x \, \psi \)
bitri l0 _