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Mirrors > Home > ILE Home > Th. List > pm2.24ii | GIF version |
Description: A contradiction implies anything. Inference from pm2.24 551. (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 575 | . 2 ⊢ (𝜑 → 𝜓) |
4 | 1, 3 | ax-mp 7 | 1 ⊢ 𝜓 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 |
This theorem was proved from axioms: ax-mp 7 ax-in2 545 |
This theorem is referenced by: (None) |
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