Theorem rblem7 1767

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 1758	. . 3 ⊢ (¬ ¬ (¬ 𝜓 ∨ 𝜑) ∨ (¬ (¬ 𝜑 ∨ 𝜓) ∨ ¬ (¬ 𝜓 ∨ 𝜑)))
3		rblem5 1765	. . 3 ⊢ (¬ (¬ ¬ (¬ 𝜓 ∨ 𝜑) ∨ (¬ (¬ 𝜑 ∨ 𝜓) ∨ ¬ (¬ 𝜓 ∨ 𝜑))) ∨ (¬ ¬ (¬ (¬ 𝜑 ∨ 𝜓) ∨ ¬ (¬ 𝜓 ∨ 𝜑)) ∨ (¬ 𝜓 ∨ 𝜑)))
4	2, 3	anmp 1755	. 2 ⊢ (¬ ¬ (¬ (¬ 𝜑 ∨ 𝜓) ∨ ¬ (¬ 𝜓 ∨ 𝜑)) ∨ (¬ 𝜓 ∨ 𝜑))
5	1, 4	anmp 1755	1 ⊢ (¬ 𝜓 ∨ 𝜑)

Syntax hints:  ¬ wn 3   ∨ wo 843

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 206  df-an 396  df-or 844

This theorem is referenced by:  re2luk1  1769  re2luk2  1770  re2luk3  1771