Theorem ee022

Description: e022 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee022.1	$$⊢\phi$$
	ee022.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
	ee022.3	$$⊢\psi \to \left(\chi \to \tau \right)$$
	ee022.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee022	$$⊢\psi \to \left(\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee022.1	$$⊢\phi$$
2		ee022.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
3		ee022.3	$$⊢\psi \to \left(\chi \to \tau \right)$$
4		ee022.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	a1i	$$⊢\chi \to \phi$$
6	5	a1i	$$⊢\psi \to \left(\chi \to \phi \right)$$
7	6 2 3 4	ee222	$$⊢\psi \to \left(\chi \to \eta \right)$$