Theorem ee30

Description: e30 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee30.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	ee30.2	$$⊢\tau$$
	ee30.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
Assertion	ee30	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee30.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ee30.2	$$⊢\tau$$
3		ee30.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
4	2	a1i	$$⊢\chi \to \tau$$
5	4	a1i	$$⊢\psi \to \left(\chi \to \tau \right)$$
6	5	a1i	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
7	1 6 3	ee33	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$