Theorem rblem3

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
Assertion	rblem3	⊢ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( ( 𝜒 ∨ 𝜓 ) ∨ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		rb-ax2	⊢ ( ¬ ( 𝜑 ∨ ( 𝜒 ∨ 𝜓 ) ) ∨ ( ( 𝜒 ∨ 𝜓 ) ∨ 𝜑 ) )
2		rblem2	⊢ ( ¬ ( 𝜑 ∨ 𝜒 ) ∨ ( 𝜑 ∨ ( 𝜒 ∨ 𝜓 ) ) )
3		rb-ax2	⊢ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( 𝜑 ∨ 𝜒 ) )
4	2 3	rbsyl	⊢ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( 𝜑 ∨ ( 𝜒 ∨ 𝜓 ) ) )
5	1 4	rbsyl	⊢ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( ( 𝜒 ∨ 𝜓 ) ∨ 𝜑 ) )