Theorem ee200

Description: e200 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee200.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee200.2	$$⊢\theta$$
	ee200.3	$$⊢\tau$$
	ee200.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee200	$$⊢\phi \to \left(\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee200.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee200.2	$$⊢\theta$$
3		ee200.3	$$⊢\tau$$
4		ee200.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	a1i	$$⊢\psi \to \theta$$
6	5	a1i	$$⊢\phi \to \left(\psi \to \theta \right)$$
7	3	a1i	$$⊢\psi \to \tau$$
8	7	a1i	$$⊢\phi \to \left(\psi \to \tau \right)$$
9	1 6 8 4	ee222	$$⊢\phi \to \left(\psi \to \eta \right)$$