Theorem ee122

Description: e122 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee122.1	$$⊢\phi \to \psi$$
	ee122.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
	ee122.3	$$⊢\phi \to \left(\chi \to \tau \right)$$
	ee122.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee122	$$⊢\phi \to \left(\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee122.1	$$⊢\phi \to \psi$$
2		ee122.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3		ee122.3	$$⊢\phi \to \left(\chi \to \tau \right)$$
4		ee122.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	a1d	$$⊢\phi \to \left(\chi \to \psi \right)$$
6	5 2 3 4	ee222	$$⊢\phi \to \left(\chi \to \eta \right)$$