Theorem ee211

Description: e211 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee211.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee211.2	$$⊢\phi \to \theta$$
	ee211.3	$$⊢\phi \to \tau$$
	ee211.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee211	$$⊢\phi \to \left(\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee211.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee211.2	$$⊢\phi \to \theta$$
3		ee211.3	$$⊢\phi \to \tau$$
4		ee211.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	a1d	$$⊢\phi \to \left(\psi \to \theta \right)$$
6	3	a1d	$$⊢\phi \to \left(\psi \to \tau \right)$$
7	1 5 6 4	ee222	$$⊢\phi \to \left(\psi \to \eta \right)$$