Theorem 19.36i

Inference associated with 19.36. See 19.36iv for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993.)

Hypotheses
19.36.1
\( \vdash \Finv x \, \psi \)
19.36i.2
\( \vdash \exists x \, (\varphi \rightarrow \psi) \)
Conclusion
\( \vdash \forall x \, \varphi \rightarrow \psi \)
Proof
l0
19.36i.2
\( \vdash \exists x \, (\varphi \rightarrow \psi) \)
19.36.1
19.36 _
\( \vdash \exists x \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, \varphi \rightarrow \psi \)
mpbi l0 _