Theorem ee002

Description: e002 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee002.1	$$⊢\phi$$
	ee002.2	$$⊢\psi$$
	ee002.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
	ee002.4	$$⊢\phi \to \left(\psi \to \left(\tau \to \eta \right)\right)$$
Assertion	ee002	$$⊢\chi \to \left(\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee002.1	$$⊢\phi$$
2		ee002.2	$$⊢\psi$$
3		ee002.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
4		ee002.4	$$⊢\phi \to \left(\psi \to \left(\tau \to \eta \right)\right)$$
5	1	a1i	$$⊢\theta \to \phi$$
6	5	a1i	$$⊢\chi \to \left(\theta \to \phi \right)$$
7	2	a1i	$$⊢\theta \to \psi$$
8	7	a1i	$$⊢\chi \to \left(\theta \to \psi \right)$$
9	6 8 3 4	ee222	$$⊢\chi \to \left(\theta \to \eta \right)$$