Theorem ee02an

Description: e02an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee02an.1	$$⊢\phi$$
	ee02an.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
	ee02an.3	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
Assertion	ee02an	$$⊢\psi \to \left(\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee02an.1	$$⊢\phi$$
2		ee02an.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
3		ee02an.3	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
4	3	ex	$$⊢\phi \to \left(\theta \to \tau \right)$$
5	1 2 4	mpsylsyld	$$⊢\psi \to \left(\chi \to \tau \right)$$