Theorem 19.21-2
Version of 19.21 with two quantifiers. (Contributed by NM,
4-Feb-2005.)
Hypotheses
19.21-2.1
\( \vdash \Finv x \, \varphi \)
19.21-2.2
\( \vdash \Finv y \, \varphi \)
Conclusion
\( \vdash \forall x \, \forall y \, (\varphi \rightarrow \psi) \leftrightarrow \varphi \rightarrow \forall x \, \forall y \, \psi \)
Proof
19.21-2.2
19.21 _
l2
albii _
\( \vdash \forall x \, \forall y \, (\varphi \rightarrow \psi) \leftrightarrow \forall x \, (\varphi \rightarrow \forall y \, \psi) \)
19.21-2.1
19.21 _
\( \vdash \forall x \, (\varphi \rightarrow \forall y \, \psi) \leftrightarrow \varphi \rightarrow \forall x \, \forall y \, \psi \)
bitri l2 _