Theorem ee020

Description: e020 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee020.1	$$⊢\phi$$
	ee020.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
	ee020.3	$$⊢\tau$$
	ee020.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee020	$$⊢\psi \to \left(\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee020.1	$$⊢\phi$$
2		ee020.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
3		ee020.3	$$⊢\tau$$
4		ee020.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	a1i	$$⊢\chi \to \phi$$
6	5	a1i	$$⊢\psi \to \left(\chi \to \phi \right)$$
7	3	a1i	$$⊢\chi \to \tau$$
8	7	a1i	$$⊢\psi \to \left(\chi \to \tau \right)$$
9	6 2 8 4	ee222	$$⊢\psi \to \left(\chi \to \eta \right)$$