Theorem 19.23vv

Theorem 19.23v extended to two variables. (Contributed by NM, 10-Aug-2004.)

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