Theorem ee01an

Description: e01an without virtual deductions. sylancr is also a form of e01an without virtual deduction, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee01an.1	$$⊢\phi$$
	ee01an.2	$$⊢\psi \to \chi$$
	ee01an.3	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
Assertion	ee01an	$$⊢\psi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ee01an.1	$$⊢\phi$$
2		ee01an.2	$$⊢\psi \to \chi$$
3		ee01an.3	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
4	1 2 3	sylancr	$$⊢\psi \to \theta$$