Description: Step 8 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | merlem4 | ⊢ ( 𝜏 → ( ( 𝜏 → 𝜑 ) → ( 𝜃 → 𝜑 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | meredith | ⊢ ( ( ( ( ( 𝜑 → 𝜑 ) → ( ¬ 𝜃 → ¬ 𝜃 ) ) → 𝜃 ) → 𝜏 ) → ( ( 𝜏 → 𝜑 ) → ( 𝜃 → 𝜑 ) ) ) | |
2 | merlem3 | ⊢ ( ( ( ( ( ( 𝜑 → 𝜑 ) → ( ¬ 𝜃 → ¬ 𝜃 ) ) → 𝜃 ) → 𝜏 ) → ( ( 𝜏 → 𝜑 ) → ( 𝜃 → 𝜑 ) ) ) → ( 𝜏 → ( ( 𝜏 → 𝜑 ) → ( 𝜃 → 𝜑 ) ) ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝜏 → ( ( 𝜏 → 𝜑 ) → ( 𝜃 → 𝜑 ) ) ) |