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Mirrors > Home > MPE Home > Th. List > pm2.24ii | Structured version Visualization version GIF version |
Description: A contradiction implies anything. Inference associated with pm2.21i 119 and pm2.24i 153. (Contributed by NM, 27-Feb-2008.) |
Ref | Expression |
---|---|
pm2.24ii.1 | ⊢ 𝜑 |
pm2.24ii.2 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
pm2.24ii | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.24ii.1 | . 2 ⊢ 𝜑 | |
2 | pm2.24ii.2 | . . 3 ⊢ ¬ 𝜑 | |
3 | 2 | pm2.21i 119 | . 2 ⊢ (𝜑 → 𝜓) |
4 | 1, 3 | ax-mp 5 | 1 ⊢ 𝜓 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-3 8 |
This theorem is referenced by: dtrucor2 5265 bj-babygodel 34522 bj-dtrucor2v 34737 dtrucor3 45817 |
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