Theorem rblem7 1528

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
rblem7.1	⊢ ¬ (¬ (¬ φ ∨ ψ) ∨ ¬ (¬ ψ ∨ φ))

Assertion

Ref	Expression
rblem7	⊢ (¬ ψ ∨ φ)

Proof of Theorem rblem7

Step	Hyp	Ref	Expression
1		rblem7.1	. 2 ⊢ ¬ (¬ (¬ φ ∨ ψ) ∨ ¬ (¬ ψ ∨ φ))
2		rb-ax3 1519	. . 3 ⊢ (¬ ¬ (¬ ψ ∨ φ) ∨ (¬ (¬ φ ∨ ψ) ∨ ¬ (¬ ψ ∨ φ)))
3		rblem5 1526	. . 3 ⊢ (¬ (¬ ¬ (¬ ψ ∨ φ) ∨ (¬ (¬ φ ∨ ψ) ∨ ¬ (¬ ψ ∨ φ))) ∨ (¬ ¬ (¬ (¬ φ ∨ ψ) ∨ ¬ (¬ ψ ∨ φ)) ∨ (¬ ψ ∨ φ)))
4	2, 3	anmp 1516	. 2 ⊢ (¬ ¬ (¬ (¬ φ ∨ ψ) ∨ ¬ (¬ ψ ∨ φ)) ∨ (¬ ψ ∨ φ))
5	1, 4	anmp 1516	1 ⊢ (¬ ψ ∨ φ)

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:  re2luk1  1530  re2luk2  1531  re2luk3  1532