Theorem e22an

Description: Conjunction form of e22 . (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e22an.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e22an.2	$$⊢\left(\phi ,\psi \to \theta \right)$$
	e22an.3	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
Assertion	e22an	$$⊢\left(\phi ,\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e22an.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e22an.2	$$⊢\left(\phi ,\psi \to \theta \right)$$
3		e22an.3	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
4	3	ex	$$⊢\chi \to \left(\theta \to \tau \right)$$
5	1 2 4	e22	$$⊢\left(\phi ,\psi \to \tau \right)$$