Theorem ee23an

Description: e23an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee23an.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee23an.2	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
	ee23an.3	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
Assertion	ee23an	$$⊢\phi \to \left(\psi \to \left(\theta \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee23an.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee23an.2	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
3		ee23an.3	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
4	1	a1dd	$$⊢\phi \to \left(\psi \to \left(\theta \to \chi \right)\right)$$
5	4 2 3	ee33an	$$⊢\phi \to \left(\psi \to \left(\theta \to \eta \right)\right)$$