Theorem 19.27

Theorem 19.27 of [Margaris] p. 90. See 19.27v for a version requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)

Hypothesis
19.27.1
\( \vdash \Finv x \, \psi \)
Conclusion
\( \vdash \forall x \, (\varphi \wedge \psi) \leftrightarrow \forall x \, \varphi \wedge \psi \)
Proof
l0
19.26
\( \vdash \forall x \, (\varphi \wedge \psi) \leftrightarrow \forall x \, \varphi \wedge \forall x \, \psi \)
19.27.1
19.3 _
anbi2i _
\( \vdash \forall x \, \varphi \wedge \forall x \, \psi \leftrightarrow \forall x \, \varphi \wedge \psi \)
bitri l0 _