Theorem ee32

Description: e32 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee32.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	ee32.2	$$⊢\phi \to \left(\psi \to \tau \right)$$
	ee32.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
Assertion	ee32	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ee32.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ee32.2	$$⊢\phi \to \left(\psi \to \tau \right)$$
3		ee32.3	$$⊢\theta \to \left(\tau \to \eta \right)$$
4	2	a1dd	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
5	1 4 3	ee33	$$⊢\phi \to \left(\psi \to \left(\chi \to \eta \right)\right)$$