Theorem e11an

Description: Conjunction form of e11 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e11an.1	$$⊢\left(\phi \to \psi \right)$$
	e11an.2	$$⊢\left(\phi \to \chi \right)$$
	e11an.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	e11an	$$⊢\left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e11an.1	$$⊢\left(\phi \to \psi \right)$$
2		e11an.2	$$⊢\left(\phi \to \chi \right)$$
3		e11an.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
4	3	ex	$$⊢\psi \to \left(\chi \to \theta \right)$$
5	1 2 4	e11	$$⊢\left(\phi \to \theta \right)$$