Theorem hbxfrbi

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. See hbxfreq for equality version. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypotheses	hbxfrbi.1	$$⊢\phi \leftrightarrow \psi$$
	hbxfrbi.2	$$⊢\psi \to \forall x\psi$$
Assertion	hbxfrbi	$$⊢\phi \to \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		hbxfrbi.1	$$⊢\phi \leftrightarrow \psi$$
2		hbxfrbi.2	$$⊢\psi \to \forall x\psi$$
3	1	albii	$$⊢\forall x\phi \leftrightarrow \forall x\psi$$
4	2 1 3	3imtr4i	$$⊢\phi \to \forall x\phi$$