Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ainaiaandna | Structured version Visualization version GIF version |
Description: Given a, a implies it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020.) |
Ref | Expression |
---|---|
ainaiaandna.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
ainaiaandna | ⊢ (𝜑 → ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ainaiaandna.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | atnaiana 43957 | . 2 ⊢ ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑)) |
3 | 2 | a1i 11 | 1 ⊢ (𝜑 → ¬ (𝜑 → (𝜑 ∧ ¬ 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 399 |
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-an 400 df-tru 1545 df-fal 1555 |
This theorem is referenced by: (None) |
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