Theorem bnj1397

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

	Ref	Expression
Hypotheses	bnj1397.1	$$⊢\phi \to \exists x\psi$$
	bnj1397.2	$$⊢\psi \to \forall x\psi$$
Assertion	bnj1397	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1397.1	$$⊢\phi \to \exists x\psi$$
2		bnj1397.2	$$⊢\psi \to \forall x\psi$$
3	2	19.9h	$$⊢\exists x\psi \leftrightarrow \psi$$
4	1 3	sylib	$$⊢\phi \to \psi$$