Theorem ee33an

Description: e33an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee33an.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	ee33an.2	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
	ee33an.3	$$⊢\left(\theta \wedge \tau \right)\to \eta$$
Assertion	ee33an	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee33an.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ee33an.2	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
3		ee33an.3	$$⊢\left(\theta \wedge \tau \right)\to \eta$$
4	3	ex	$$⊢\theta \to \left(\tau \to \eta \right)$$
5	1 2 4	ee33	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$