Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | ax3 | ⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( 𝜓 → 𝜑 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | luklem2 | ⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) → ( 𝜓 → 𝜑 ) ) ) | |
2 | luklem4 | ⊢ ( ( ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) → ( 𝜓 → 𝜑 ) ) → ( 𝜓 → 𝜑 ) ) | |
3 | 1 2 | luklem1 | ⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( 𝜓 → 𝜑 ) ) |