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.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | rblem7.1 | ⊢ ¬ ( ¬ ( ¬ 𝜑 ∨ 𝜓 ) ∨ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ) | |
| Assertion | rblem7 | ⊢ ( ¬ 𝜓 ∨ 𝜑 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rblem7.1 | ⊢ ¬ ( ¬ ( ¬ 𝜑 ∨ 𝜓 ) ∨ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ) | |
| 2 | rb-ax3 | ⊢ ( ¬ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ∨ ( ¬ ( ¬ 𝜑 ∨ 𝜓 ) ∨ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ) ) | |
| 3 | rblem5 | ⊢ ( ¬ ( ¬ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ∨ ( ¬ ( ¬ 𝜑 ∨ 𝜓 ) ∨ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ) ) ∨ ( ¬ ¬ ( ¬ ( ¬ 𝜑 ∨ 𝜓 ) ∨ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ) ∨ ( ¬ 𝜓 ∨ 𝜑 ) ) ) | |
| 4 | 2 3 | anmp | ⊢ ( ¬ ¬ ( ¬ ( ¬ 𝜑 ∨ 𝜓 ) ∨ ¬ ( ¬ 𝜓 ∨ 𝜑 ) ) ∨ ( ¬ 𝜓 ∨ 𝜑 ) ) |
| 5 | 1 4 | anmp | ⊢ ( ¬ 𝜓 ∨ 𝜑 ) |