Theorem ee112

Description: e112 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee112.1	$$⊢\phi \to \psi$$
	ee112.2	$$⊢\phi \to \chi$$
	ee112.3	$$⊢\phi \to \left(\theta \to \tau \right)$$
	ee112.4	$$⊢\psi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
Assertion	ee112	$$⊢\phi \to \left(\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee112.1	$$⊢\phi \to \psi$$
2		ee112.2	$$⊢\phi \to \chi$$
3		ee112.3	$$⊢\phi \to \left(\theta \to \tau \right)$$
4		ee112.4	$$⊢\psi \to \left(\chi \to \left(\tau \to \eta \right)\right)$$
5	1	a1d	$$⊢\phi \to \left(\theta \to \psi \right)$$
6	2	a1d	$$⊢\phi \to \left(\theta \to \chi \right)$$
7	5 6 3 4	ee222	$$⊢\phi \to \left(\theta \to \eta \right)$$