Theorem ee03

Description: e03 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee03.1	$$⊢\phi$$
	ee03.2	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
	ee03.3	$$⊢\phi \to \left(\tau \to \eta \right)$$
Assertion	ee03	$$⊢\psi \to \left(\chi \to \left(\theta \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee03.1	$$⊢\phi$$
2		ee03.2	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
3		ee03.3	$$⊢\phi \to \left(\tau \to \eta \right)$$
4	1	a1i	$$⊢\psi \to \phi$$
5	4	a1d	$$⊢\psi \to \left(\chi \to \phi \right)$$
6	5	a1dd	$$⊢\psi \to \left(\chi \to \left(\theta \to \phi \right)\right)$$
7	6 2 3	ee33	$$⊢\psi \to \left(\chi \to \left(\theta \to \eta \right)\right)$$