Theorem rb-ax4

Description: The fourth 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-ax4	$$⊢\left(\neg \left(\phi \vee \phi \right)\vee \phi \right)$$

Proof

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