Theorem rblem2

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	rblem2	⊢ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( 𝜒 ∨ ( 𝜑 ∨ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		rb-ax2	⊢ ( ¬ ( 𝜓 ∨ 𝜑 ) ∨ ( 𝜑 ∨ 𝜓 ) )
2		rb-ax3	⊢ ( ¬ 𝜑 ∨ ( 𝜓 ∨ 𝜑 ) )
3	1 2	rbsyl	⊢ ( ¬ 𝜑 ∨ ( 𝜑 ∨ 𝜓 ) )
4		rb-ax1	⊢ ( ¬ ( ¬ 𝜑 ∨ ( 𝜑 ∨ 𝜓 ) ) ∨ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( 𝜒 ∨ ( 𝜑 ∨ 𝜓 ) ) ) )
5	3 4	anmp	⊢ ( ¬ ( 𝜒 ∨ 𝜑 ) ∨ ( 𝜒 ∨ ( 𝜑 ∨ 𝜓 ) ) )