Theorem rblem3 1524

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 1518	. 2 ⊢ (¬ (φ ∨ (χ ∨ ψ)) ∨ ((χ ∨ ψ) ∨ φ))
2		rblem2 1523	. . 3 ⊢ (¬ (φ ∨ χ) ∨ (φ ∨ (χ ∨ ψ)))
3		rb-ax2 1518	. . 3 ⊢ (¬ (χ ∨ φ) ∨ (φ ∨ χ))
4	2, 3	rbsyl 1521	. 2 ⊢ (¬ (χ ∨ φ) ∨ (φ ∨ (χ ∨ ψ)))
5	1, 4	rbsyl 1521	1 ⊢ (¬ (χ ∨ φ) ∨ ((χ ∨ ψ) ∨ φ))

Syntax hints:  ¬ wn 3   ∨ wo 357

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 177  df-or 359  df-an 360

This theorem is referenced by:  rblem6  1527