Theorem 19.19

Theorem 19.19 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Hypothesis
19.19.1
\( \vdash \Finv x \, \varphi \)
Conclusion
\( \vdash \forall x \, (\varphi \leftrightarrow \psi) \rightarrow (\varphi \leftrightarrow \exists x \, \psi) \)
Proof
19.19.1
l1
19.9 _
\( \vdash \exists x \, \varphi \leftrightarrow \varphi \)
exbi
\( \vdash \forall x \, (\varphi \leftrightarrow \psi) \rightarrow (\exists x \, \varphi \leftrightarrow \exists x \, \psi) \)
bitr3id l1 _