Theorem e02an

Description: Conjunction form of e02 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e02an.1	$$⊢\phi$$
	e02an.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
	e02an.3	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
Assertion	e02an	$$⊢\left(\psi ,\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e02an.1	$$⊢\phi$$
2		e02an.2	$$⊢\left(\psi ,\chi \to \theta \right)$$
3		e02an.3	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
4	3	ex	$$⊢\phi \to \left(\theta \to \tau \right)$$
5	1 2 4	e02	$$⊢\left(\psi ,\chi \to \tau \right)$$