Theorem 19.45

Theorem 19.45 of [Margaris] p. 90. See 19.45v for a version requiring fewer axioms. (Contributed by NM, 12-Mar-1993.)

Hypothesis
19.45.1
\( \vdash \Finv x \, \varphi \)
Conclusion
\( \vdash \exists x \, (\varphi \vee \psi) \leftrightarrow \varphi \vee \exists x \, \psi \)
Proof
l0
19.43
\( \vdash \exists x \, (\varphi \vee \psi) \leftrightarrow \exists x \, \varphi \vee \exists x \, \psi \)
19.45.1
19.9 _
orbi1i _
\( \vdash \exists x \, \varphi \vee \exists x \, \psi \leftrightarrow \varphi \vee \exists x \, \psi \)
bitri l0 _