Theorem 19.26-2
Theorem 19.26 with two quantifiers. (Contributed by NM, 3-Feb-2005.)
Conclusion
\( \vdash \forall x \, \forall y \, (\varphi \wedge \psi) \leftrightarrow \forall x \, \forall y \, \varphi \wedge \forall x \, \forall y \, \psi \)
Proof
19.26
l1
albii _
\( \vdash \forall x \, \forall y \, (\varphi \wedge \psi) \leftrightarrow \forall x \, (\forall y \, \varphi \wedge \forall y \, \psi) \)
19.26
\( \vdash \forall x \, (\forall y \, \varphi \wedge \forall y \, \psi) \leftrightarrow \forall x \, \forall y \, \varphi \wedge \forall x \, \forall y \, \psi \)
bitri l1 _