Theorem ee221

Description: e221 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee221.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee221.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
	ee221.3	$$⊢\phi \to \tau$$
	ee221.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee221	$$⊢\phi \to \left(\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee221.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee221.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
3		ee221.3	$$⊢\phi \to \tau$$
4		ee221.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	3	a1d	$$⊢\phi \to \left(\psi \to \tau \right)$$
6	1 2 5 4	ee222	$$⊢\phi \to \left(\psi \to \eta \right)$$