Theorem ee100

Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee100.1	$$⊢\phi \to \psi$$
	ee100.2	$$⊢\chi$$
	ee100.3	$$⊢\theta$$
	ee100.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	ee100	$$⊢\phi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		ee100.1	$$⊢\phi \to \psi$$
2		ee100.2	$$⊢\chi$$
3		ee100.3	$$⊢\theta$$
4		ee100.4	$$⊢\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	2	a1i	$$⊢\phi \to \chi$$
6	3	a1i	$$⊢\phi \to \theta$$
7	1 5 6 4	syl3c	$$⊢\phi \to \tau$$