Theorem 19.9h

A wff may be existentially quantified with a variable not free in it. Theorem 19.9 of [Margaris] p. 89. (Contributed by FL, 24-Mar-2007.) (Proof shortened by Wolf Lammen, 5-Jan-2018.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)

Hypothesis
19.9h.1
\( \vdash \varphi \rightarrow \forall x \, \varphi \)
Conclusion
\( \vdash \exists x \, \varphi \leftrightarrow \varphi \)
Proof
19.9h.1
nf5i _
19.9 _