Theorem 19.37

Theorem 19.37 of [Margaris] p. 90. See 19.37v for a version requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)

Hypothesis
19.37.1
\( \vdash \Finv x \, \varphi \)
Conclusion
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \varphi \rightarrow \exists x \, \psi \)
Proof
l0
19.35
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, \varphi \rightarrow \exists x \, \psi \)
19.37.1
19.3 _
imbi1i _
\( \vdash \forall x \, \varphi \rightarrow \exists x \, \psi \leftrightarrow \varphi \rightarrow \exists x \, \psi \)
bitri l0 _