Theorem ee012

Description: e012 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee012.1	$$⊢\phi$$
	ee012.2	$$⊢\psi \to \chi$$
	ee012.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
	ee012.4	$$⊢\phi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
Assertion	ee012	$$⊢\psi \to \left(\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee012.1	$$⊢\phi$$
2		ee012.2	$$⊢\psi \to \chi$$
3		ee012.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
4		ee012.4	$$⊢\phi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
5	1	a1i	$$⊢\theta \to \phi$$
6	5	a1i	$$⊢\psi \to \left(\theta \to \phi \right)$$
7	2	a1d	$$⊢\psi \to \left(\theta \to \chi \right)$$
8	6 7 3 4	ee222	$$⊢\psi \to \left(\theta \to \eta \right)$$