Description: Recover ax-3 from hirstL-ax3 . (Contributed by Jarvin Udandy, 3-Jul-2015) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | ax3h | ⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( 𝜓 → 𝜑 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hirstL-ax3 | ⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( ( ¬ 𝜑 → 𝜓 ) → 𝜑 ) ) | |
2 | jarr | ⊢ ( ( ( ¬ 𝜑 → 𝜓 ) → 𝜑 ) → ( 𝜓 → 𝜑 ) ) | |
3 | 1 2 | syl | ⊢ ( ( ¬ 𝜑 → ¬ 𝜓 ) → ( 𝜓 → 𝜑 ) ) |