Theorem ee021

Description: e021 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee021.1	$$⊢\phi$$
	ee021.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
	ee021.3	$$⊢\psi \to \tau$$
	ee021.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee021	$$⊢\psi \to \left(\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee021.1	$$⊢\phi$$
2		ee021.2	$$⊢\psi \to \left(\chi \to \theta \right)$$
3		ee021.3	$$⊢\psi \to \tau$$
4		ee021.4	$$⊢\phi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	a1i	$$⊢\chi \to \phi$$
6	5	a1i	$$⊢\psi \to \left(\chi \to \phi \right)$$
7	3	a1d	$$⊢\psi \to \left(\chi \to \tau \right)$$
8	6 2 7 4	ee222	$$⊢\psi \to \left(\chi \to \eta \right)$$