Theorem ee101

Description: e101 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee101.1	$$⊢\phi \to \psi$$
	ee101.2	$$⊢\chi$$
	ee101.3	$$⊢\phi \to \theta$$
	ee101.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	ee101	$$⊢\phi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		ee101.1	$$⊢\phi \to \psi$$
2		ee101.2	$$⊢\chi$$
3		ee101.3	$$⊢\phi \to \theta$$
4		ee101.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	2	a1i	$$⊢\phi \to \chi$$
6	1 5 3 4	syl3c	$$⊢\phi \to \tau$$