Theorem rblem2 1683

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
rblem2	⊢ (¬ (𝜒 ∨ 𝜑) ∨ (𝜒 ∨ (𝜑 ∨ 𝜓)))

Proof of Theorem rblem2

Step	Hyp	Ref	Expression
1		rb-ax2 1678	. . 3 ⊢ (¬ (𝜓 ∨ 𝜑) ∨ (𝜑 ∨ 𝜓))
2		rb-ax3 1679	. . 3 ⊢ (¬ 𝜑 ∨ (𝜓 ∨ 𝜑))
3	1, 2	rbsyl 1681	. 2 ⊢ (¬ 𝜑 ∨ (𝜑 ∨ 𝜓))
4		rb-ax1 1677	. 2 ⊢ (¬ (¬ 𝜑 ∨ (𝜑 ∨ 𝜓)) ∨ (¬ (𝜒 ∨ 𝜑) ∨ (𝜒 ∨ (𝜑 ∨ 𝜓))))
5	3, 4	anmp 1676	1 ⊢ (¬ (𝜒 ∨ 𝜑) ∨ (𝜒 ∨ (𝜑 ∨ 𝜓)))

Syntax hints:  ¬ wn 3   ∨ wo 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by:  rblem3  1684  rblem4  1685  re2luk3  1692