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Mirrors > Home > ILE Home > Th. List > bifal | GIF version |
Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015.) |
Ref | Expression |
---|---|
bifal.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
bifal | ⊢ (𝜑 ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bifal.1 | . 2 ⊢ ¬ 𝜑 | |
2 | fal 1360 | . 2 ⊢ ¬ ⊥ | |
3 | 1, 2 | 2false 701 | 1 ⊢ (𝜑 ↔ ⊥) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 105 ⊥wfal 1358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 |
This theorem is referenced by: (None) |
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