Theorem 19.28

Theorem 19.28 of [Margaris] p. 90. See 19.28v for a version requiring fewer axioms. (Contributed by NM, 1-Aug-1993.) (Proof shortened by Wolf Lammen, 7-May-2025.)

Hypothesis
19.28.1
\( \vdash \Finv x \, \varphi \)
Conclusion
\( \vdash \forall x \, (\varphi \wedge \psi) \leftrightarrow \varphi \wedge \forall x \, \psi \)
Proof
l0
19.26
\( \vdash \forall x \, (\varphi \wedge \psi) \leftrightarrow \forall x \, \varphi \wedge \forall x \, \psi \)
19.28.1
19.3 _
\( \vdash \forall x \, \varphi \leftrightarrow \varphi \)
bianbi l0 _