Theorem wl-impchain-com-1.4

Description: This theorem is in fact a copy of com14 , and repeated here to demonstrate a simple proof scheme. The number '4' in the theorem name indicates that a chain of length 4 is modified.

See wl-impchain-com-1.x for more information how this proof is generated. (Contributed by Wolf Lammen, 7-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	wl-impchain-com-1.4.h1	$$⊢\eta \to \left(\theta \to \left(\chi \to \left(\psi \to \phi \right)\right)\right)$$
Assertion	wl-impchain-com-1.4	$$⊢\psi \to \left(\theta \to \left(\chi \to \left(\eta \to \phi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-impchain-com-1.4.h1	$$⊢\eta \to \left(\theta \to \left(\chi \to \left(\psi \to \phi \right)\right)\right)$$
2	1	wl-impchain-com-1.3	$$⊢\chi \to \left(\theta \to \left(\eta \to \left(\psi \to \phi \right)\right)\right)$$
3		wl-luk-pm2.04	$$⊢\left(\eta \to \left(\psi \to \phi \right)\right)\to \left(\psi \to \left(\eta \to \phi \right)\right)$$
4	2 3	wl-impchain-mp-2	$$⊢\chi \to \left(\theta \to \left(\psi \to \left(\eta \to \phi \right)\right)\right)$$
5	4	wl-impchain-com-1.3	$$⊢\psi \to \left(\theta \to \left(\chi \to \left(\eta \to \phi \right)\right)\right)$$