Theorem e01an

Description: Conjunction form of e01 . (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e01an.1	$$⊢\phi$$
	e01an.2	$$⊢\left(\psi \to \chi \right)$$
	e01an.3	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
Assertion	e01an	$$⊢\left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e01an.1	$$⊢\phi$$
2		e01an.2	$$⊢\left(\psi \to \chi \right)$$
3		e01an.3	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
4	3	ex	$$⊢\phi \to \left(\chi \to \theta \right)$$
5	1 2 4	e01	$$⊢\left(\psi \to \theta \right)$$