Theorem ee120

Description: Virtual deduction rule e120 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee120.1	$$⊢\phi \to \psi$$
	ee120.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
	ee120.3	$$⊢\tau$$
	ee120.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	ee120	$$⊢\phi \to \left(\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		ee120.1	$$⊢\phi \to \psi$$
2		ee120.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3		ee120.3	$$⊢\tau$$
4		ee120.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	a1d	$$⊢\phi \to \left(\chi \to \psi \right)$$
6	3	a1i	$$⊢\chi \to \tau$$
7	6	a1i	$$⊢\phi \to \left(\chi \to \tau \right)$$
8	5 2 7 4	ee222	$$⊢\phi \to \left(\chi \to \eta \right)$$