Theorem rblem3 1792

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.)

Assertion

Ref	Expression
rblem3	⊢ (¬ (𝜒 ∨ 𝜑) ∨ ((𝜒 ∨ 𝜓) ∨ 𝜑))

Proof of Theorem rblem3

Step	Hyp	Ref	Expression
1		rb-ax2 1786	. 2 ⊢ (¬ (𝜑 ∨ (𝜒 ∨ 𝜓)) ∨ ((𝜒 ∨ 𝜓) ∨ 𝜑))
2		rblem2 1791	. . 3 ⊢ (¬ (𝜑 ∨ 𝜒) ∨ (𝜑 ∨ (𝜒 ∨ 𝜓)))
3		rb-ax2 1786	. . 3 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ (𝜑 ∨ 𝜒))
4	2, 3	rbsyl 1789	. 2 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ (𝜑 ∨ (𝜒 ∨ 𝜓)))
5	1, 4	rbsyl 1789	1 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ ((𝜒 ∨ 𝜓) ∨ 𝜑))

This proof depends on syntax axioms:  ¬ wn 3   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by:  rblem6  1795