Theorem e10an

Description: Conjunction form of e10 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e10an.1	$$⊢\left(\phi \to \psi \right)$$
	e10an.2	$$⊢\chi$$
	e10an.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
Assertion	e10an	$$⊢\left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e10an.1	$$⊢\left(\phi \to \psi \right)$$
2		e10an.2	$$⊢\chi$$
3		e10an.3	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
4	3	ex	$$⊢\psi \to \left(\chi \to \theta \right)$$
5	1 2 4	e10	$$⊢\left(\phi \to \theta \right)$$