Theorem ee220

Description: e220 without virtual deductions. (Contributed by Alan Sare, 12-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee220.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee220.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
	ee220.3	$$⊢\tau$$
	ee220.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee220	$$⊢\phi \to \left(\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee220.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee220.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
3		ee220.3	$$⊢\tau$$
4		ee220.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	3	2a1i	$$⊢\phi \to \left(\psi \to \tau \right)$$
6	1 2 5 4	ee222	$$⊢\phi \to \left(\psi \to \eta \right)$$