Theorem e33an

Description: Conjunction form of e33 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e33an.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
	e33an.2	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$
	e33an.3	$$⊢\left(\theta \wedge \tau \right)\to \eta$$
Assertion	e33an	$$⊢\left(\phi ,\psi ,\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e33an.1	$$⊢\left(\phi ,\psi ,\chi \to \theta \right)$$
2		e33an.2	$$⊢\left(\phi ,\psi ,\chi \to \tau \right)$$
3		e33an.3	$$⊢\left(\theta \wedge \tau \right)\to \eta$$
4	3	ex	$$⊢\theta \to \left(\tau \to \eta \right)$$
5	1 2 4	e33	$$⊢\left(\phi ,\psi ,\chi \to \eta \right)$$