Theorem e03an

Description: Conjunction form of e03 . (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e03an.1	$$⊢\phi$$
	e03an.2	$$⊢\left(\psi ,\chi ,\theta \to \tau \right)$$
	e03an.3	$$⊢\left(\phi \wedge \tau \right)\to \eta$$
Assertion	e03an	$$⊢\left(\psi ,\chi ,\theta \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e03an.1	$$⊢\phi$$
2		e03an.2	$$⊢\left(\psi ,\chi ,\theta \to \tau \right)$$
3		e03an.3	$$⊢\left(\phi \wedge \tau \right)\to \eta$$
4	3	ex	$$⊢\phi \to \left(\tau \to \eta \right)$$
5	1 2 4	e03	$$⊢\left(\psi ,\chi ,\theta \to \eta \right)$$