Theorem ee110

Description: e110 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee110.1	$$⊢\phi \to \psi$$
	ee110.2	$$⊢\phi \to \chi$$
	ee110.3	$$⊢\theta$$
	ee110.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	ee110	$$⊢\phi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		ee110.1	$$⊢\phi \to \psi$$
2		ee110.2	$$⊢\phi \to \chi$$
3		ee110.3	$$⊢\theta$$
4		ee110.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	3	a1i	$$⊢\phi \to \theta$$
6	1 2 5 4	syl3c	$$⊢\phi \to \tau$$