Theorem rbsyl

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
Hypotheses	rbsyl.1	⊢ ( ¬ 𝜓 ∨ 𝜒 )
	rbsyl.2	⊢ ( 𝜑 ∨ 𝜓 )
Assertion	rbsyl	⊢ ( 𝜑 ∨ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		rbsyl.1	⊢ ( ¬ 𝜓 ∨ 𝜒 )
2		rbsyl.2	⊢ ( 𝜑 ∨ 𝜓 )
3		rb-ax1	⊢ ( ¬ ( ¬ 𝜓 ∨ 𝜒 ) ∨ ( ¬ ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜑 ∨ 𝜒 ) ) )
4	1 3	anmp	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) ∨ ( 𝜑 ∨ 𝜒 ) )
5	2 4	anmp	⊢ ( 𝜑 ∨ 𝜒 )