Theorem rb-ax3

Description: The third 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-ax3	⊢ ( ¬ 𝜑 ∨ ( 𝜓 ∨ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.46	⊢ ( ¬ ( 𝜓 ∨ 𝜑 ) → ¬ 𝜑 )
2	1	con1i	⊢ ( ¬ ¬ 𝜑 → ( 𝜓 ∨ 𝜑 ) )
3	2	orri	⊢ ( ¬ 𝜑 ∨ ( 𝜓 ∨ 𝜑 ) )