Theorem ee03an

Description: Conjunction form of ee03 . (Contributed by Alan Sare, 18-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee03an.1	$$⊢\phi$$
	ee03an.2	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
	ee03an.3	$$⊢\left(\phi \wedge \tau \right)\to \eta$$
Assertion	ee03an	$$⊢\psi \to \left(\chi \to \left(\theta \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee03an.1	$$⊢\phi$$
2		ee03an.2	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
3		ee03an.3	$$⊢\left(\phi \wedge \tau \right)\to \eta$$
4	3	ex	$$⊢\phi \to \left(\tau \to \eta \right)$$
5	1 2 4	ee03	$$⊢\psi \to \left(\chi \to \left(\theta \to \eta \right)\right)$$