Theorem 19.9h

Description: 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)

	Ref	Expression
Hypothesis	19.9h.1	$$⊢\phi \to \forall x\phi$$
Assertion	19.9h	$$⊢\exists x\phi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		19.9h.1	$$⊢\phi \to \forall x\phi$$
2	1	nf5i	$$⊢Ⅎx\phi$$
3	2	19.9	$$⊢\exists x\phi \leftrightarrow \phi$$