Theorem ggen31

Description: gen31 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ggen31.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	ggen31	$$⊢\phi \to \left(\psi \to \left(\chi \to \forall x\theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ggen31.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2	1	imp	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \theta \right)$$
3	2	alrimdv	$$⊢\left(\phi \wedge \psi \right)\to \left(\chi \to \forall x\theta \right)$$
4	3	ex	$$⊢\phi \to \left(\psi \to \left(\chi \to \forall x\theta \right)\right)$$