Theorem rb-ax2

Description: The second of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	rb-ax2	$$⊢\left(\neg \left(\phi \vee \psi \right)\vee \left(\psi \vee \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm1.4	$$⊢\left(\phi \vee \psi \right)\to \left(\psi \vee \phi \right)$$
2	1	con3i	$$⊢\neg \left(\psi \vee \phi \right)\to \neg \left(\phi \vee \psi \right)$$
3	2	con1i	$$⊢\neg \neg \left(\phi \vee \psi \right)\to \left(\psi \vee \phi \right)$$
4	3	orri	$$⊢\left(\neg \left(\phi \vee \psi \right)\vee \left(\psi \vee \phi \right)\right)$$