Theorem ee21an

Description: e21an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee21an.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee21an.2	$$⊢\phi \to \theta$$
	ee21an.3	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
Assertion	ee21an	$$⊢\phi \to \left(\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee21an.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee21an.2	$$⊢\phi \to \theta$$
3		ee21an.3	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
4	3	ex	$$⊢\chi \to \left(\theta \to \tau \right)$$
5	1 2 4	syl6ci	$$⊢\phi \to \left(\psi \to \tau \right)$$