Theorem bnj1131

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1131.1	$$⊢\phi \to \forall x\phi$$
	bnj1131.2	$$⊢\exists x\phi$$
Assertion	bnj1131	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1131.1	$$⊢\phi \to \forall x\phi$$
2		bnj1131.2	$$⊢\exists x\phi$$
3	1	19.9h	$$⊢\exists x\phi \leftrightarrow \phi$$
4	2 3	mpbi	$$⊢\phi$$