Theorem ee210

Description: e210 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee210.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee210.2	$$⊢\phi \to \theta$$
	ee210.3	$$⊢\tau$$
	ee210.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee210	$$⊢\phi \to \left(\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee210.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee210.2	$$⊢\phi \to \theta$$
3		ee210.3	$$⊢\tau$$
4		ee210.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	a1d	$$⊢\phi \to \left(\psi \to \theta \right)$$
6	3	a1i	$$⊢\psi \to \tau$$
7	6	a1i	$$⊢\phi \to \left(\psi \to \tau \right)$$
8	1 5 7 4	ee222	$$⊢\phi \to \left(\psi \to \eta \right)$$