Theorem ee22an

Description: e22an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee22an.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee22an.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
	ee22an.3	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
Assertion	ee22an	$$⊢\phi \to \left(\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee22an.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee22an.2	$$⊢\phi \to \left(\psi \to \theta \right)$$
3		ee22an.3	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
4	3	ex	$$⊢\chi \to \left(\theta \to \tau \right)$$
5	1 2 4	syl6c	$$⊢\phi \to \left(\psi \to \tau \right)$$