Theorem ee30an

Description: Conjunction form of ee30 . (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee30an.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	ee30an.2	$$⊢\tau$$
	ee30an.3	$$⊢\left(\theta \wedge \tau \right)\to \eta$$
Assertion	ee30an	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee30an.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ee30an.2	$$⊢\tau$$
3		ee30an.3	$$⊢\left(\theta \wedge \tau \right)\to \eta$$
4	3	ex	$$⊢\theta \to \left(\tau \to \eta \right)$$
5	1 2 4	ee30	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$