Theorem rblem3

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	rblem3	$$⊢\left(\neg \left(\chi \vee \phi \right)\vee \left(\left(\chi \vee \psi \right)\vee \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		rb-ax2	$$⊢\left(\neg \left(\phi \vee \left(\chi \vee \psi \right)\right)\vee \left(\left(\chi \vee \psi \right)\vee \phi \right)\right)$$
2		rblem2	$$⊢\left(\neg \left(\phi \vee \chi \right)\vee \left(\phi \vee \left(\chi \vee \psi \right)\right)\right)$$
3		rb-ax2	$$⊢\left(\neg \left(\chi \vee \phi \right)\vee \left(\phi \vee \chi \right)\right)$$
4	2 3	rbsyl	$$⊢\left(\neg \left(\chi \vee \phi \right)\vee \left(\phi \vee \left(\chi \vee \psi \right)\right)\right)$$
5	1 4	rbsyl	$$⊢\left(\neg \left(\chi \vee \phi \right)\vee \left(\left(\chi \vee \psi \right)\vee \phi \right)\right)$$