Theorem ee212

Description: e212 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee212.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	ee212.2	$$⊢\phi \to \theta$$
	ee212.3	$$⊢\phi \to \left(\psi \to \tau \right)$$
	ee212.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee212	$$⊢\phi \to \left(\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee212.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ee212.2	$$⊢\phi \to \theta$$
3		ee212.3	$$⊢\phi \to \left(\psi \to \tau \right)$$
4		ee212.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	a1d	$$⊢\phi \to \left(\psi \to \theta \right)$$
6	1 5 3 4	ee222	$$⊢\phi \to \left(\psi \to \eta \right)$$