Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax3h | Structured version Visualization version GIF version |
Description: Recover ax-3 8 from hirstL-ax3 43926. (Contributed by Jarvin Udandy, 3-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax3h | ⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hirstL-ax3 43926 | . 2 ⊢ ((¬ 𝜑 → ¬ 𝜓) → ((¬ 𝜑 → 𝜓) → 𝜑)) | |
2 | jarr 106 | . 2 ⊢ (((¬ 𝜑 → 𝜓) → 𝜑) → (𝜓 → 𝜑)) | |
3 | 1, 2 | syl 17 | 1 ⊢ ((¬ 𝜑 → ¬ 𝜓) → (𝜓 → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
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 210 df-or 847 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |