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Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > atnaiana | Structured version Visualization version GIF version |
Description: Given a, it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020.) |
Ref | Expression |
---|---|
atnaiana.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
atnaiana | ⊢ ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | atnaiana.1 | . . . 4 ⊢ 𝜑 | |
2 | 1 | bitru 1487 | . . 3 ⊢ (𝜑 ↔ ⊤) |
3 | pm3.24 922 | . . . 4 ⊢ ¬ (𝜑 ∧ ¬ 𝜑) | |
4 | 3 | bifal 1488 | . . 3 ⊢ ((𝜑 ∧ ¬ 𝜑) ↔ ⊥) |
5 | 2, 4 | aifftbifffaibif 39737 | . 2 ⊢ ((𝜑 → (𝜑 ∧ ¬ 𝜑)) ↔ ⊥) |
6 | 5 | aisfina 39714 | 1 ⊢ ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 383 |
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 196 df-an 385 df-tru 1478 df-fal 1481 |
This theorem is referenced by: ainaiaandna 39740 confun5 39759 |
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