Theorem bnj1096

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

	Ref	Expression
Hypotheses	bnj1096.1	$$⊢\phi \to \forall x\phi$$
	bnj1096.2	$$⊢\psi \leftrightarrow \left(\chi \wedge \theta \wedge \tau \wedge \phi \right)$$
Assertion	bnj1096	$$⊢\psi \to \forall x\psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1096.1	$$⊢\phi \to \forall x\phi$$
2		bnj1096.2	$$⊢\psi \leftrightarrow \left(\chi \wedge \theta \wedge \tau \wedge \phi \right)$$
3		ax-5	$$⊢\chi \to \forall x\chi$$
4		ax-5	$$⊢\theta \to \forall x\theta$$
5		ax-5	$$⊢\tau \to \forall x\tau$$
6	3 4 5 1	bnj982	$$⊢\left(\chi \wedge \theta \wedge \tau \wedge \phi \right)\to \forall x\left(\chi \wedge \theta \wedge \tau \wedge \phi \right)$$
7	2 6	hbxfrbi	$$⊢\psi \to \forall x\psi$$