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	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜓 ∨ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		pm1.4	⊢ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜓 ∨ 𝜑 ) )
2	1	con3i	⊢ ( ¬ ( 𝜓 ∨ 𝜑 ) → ¬ ( 𝜑 ∨ 𝜓 ) )
3	2	con1i	⊢ ( ¬ ¬ ( 𝜑 ∨ 𝜓 ) → ( 𝜓 ∨ 𝜑 ) )
4	3	orri	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜓 ∨ 𝜑 ) )