Theorem ee323

Description: e323 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee323.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	ee323.2	$$⊢\phi \to \left(\psi \to \tau \right)$$
	ee323.3	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$
	ee323.4	$$⊢\theta \to \left(\tau \to \left(\eta \to \zeta \right)\right)$$
Assertion	ee323	$$⊢\phi \to \left(\psi \to \left(\chi \to \zeta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee323.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ee323.2	$$⊢\phi \to \left(\psi \to \tau \right)$$
3		ee323.3	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$
4		ee323.4	$$⊢\theta \to \left(\tau \to \left(\eta \to \zeta \right)\right)$$
5	2	a1dd	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
6	1 5 3 4	ee333	$$⊢\phi \to \left(\psi \to \left(\chi \to \zeta \right)\right)$$