Theorem 19.36

Theorem 19.36 of [Margaris] p. 90. See 19.36v for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993.)

Hypothesis
19.36.1
\( \vdash \Finv x \, \psi \)
Conclusion
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, \varphi \rightarrow \psi \)
Proof
l0
19.35
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, \varphi \rightarrow \exists x \, \psi \)
19.36.1
19.9 _
imbi2i _
\( \vdash \forall x \, \varphi \rightarrow \exists x \, \psi \leftrightarrow \forall x \, \varphi \rightarrow \psi \)
bitri l0 _