Theorem ee011

Description: e011 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee011.1	$$⊢\phi$$
	ee011.2	$$⊢\psi \to \chi$$
	ee011.3	$$⊢\psi \to \theta$$
	ee011.4	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
Assertion	ee011	$$⊢\psi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		ee011.1	$$⊢\phi$$
2		ee011.2	$$⊢\psi \to \chi$$
3		ee011.3	$$⊢\psi \to \theta$$
4		ee011.4	$$⊢\phi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	1	a1i	$$⊢\psi \to \phi$$
6	5 2 3 4	syl3c	$$⊢\psi \to \tau$$