Theorem rblem2

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	rblem2	$$⊢\left(\neg \left(\chi \vee \phi \right)\vee \left(\chi \vee \left(\phi \vee \psi \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		rb-ax2	$$⊢\left(\neg \left(\psi \vee \phi \right)\vee \left(\phi \vee \psi \right)\right)$$
2		rb-ax3	$$⊢\left(\neg \phi \vee \left(\psi \vee \phi \right)\right)$$
3	1 2	rbsyl	$$⊢\left(\neg \phi \vee \left(\phi \vee \psi \right)\right)$$
4		rb-ax1	$$⊢\left(\neg \left(\neg \phi \vee \left(\phi \vee \psi \right)\right)\vee \left(\neg \left(\chi \vee \phi \right)\vee \left(\chi \vee \left(\phi \vee \psi \right)\right)\right)\right)$$
5	3 4	anmp	$$⊢\left(\neg \left(\chi \vee \phi \right)\vee \left(\chi \vee \left(\phi \vee \psi \right)\right)\right)$$