Theorem rblem2 1523

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 1518	. . 3 ⊢ (¬ (ψ ∨ φ) ∨ (φ ∨ ψ))
2		rb-ax3 1519	. . 3 ⊢ (¬ φ ∨ (ψ ∨ φ))
3	1, 2	rbsyl 1521	. 2 ⊢ (¬ φ ∨ (φ ∨ ψ))
4		rb-ax1 1517	. 2 ⊢ (¬ (¬ φ ∨ (φ ∨ ψ)) ∨ (¬ (χ ∨ φ) ∨ (χ ∨ (φ ∨ ψ))))
5	3, 4	anmp 1516	1 ⊢ (¬ (χ ∨ φ) ∨ (χ ∨ (φ ∨ ψ)))

This proof depends on syntax axioms:  ¬ wn 3   ∨ wo 357

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

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is used by:  rblem3  1524  rblem4  1525  re2luk3  1532