Theorem pm11.53v

Version of pm11.53 with a disjoint variable condition, requiring fewer axioms. (Contributed by BJ, 7-Mar-2020.)

Conclusion
\( \vdash \forall x \, \forall y \, (\varphi \rightarrow \psi) \leftrightarrow \exists x \, \varphi \rightarrow \forall y \, \psi \)
Proof
19.21v
l1
albii _
\( \vdash \forall x \, \forall y \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, (\varphi \rightarrow \forall y \, \psi) \)
19.23v
\( \vdash \forall x \, (\varphi \rightarrow \forall y \, \psi) \leftrightarrow \exists x \, \varphi \rightarrow \forall y \, \psi \)
bitri l1 _