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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-frege41 | Structured version Visualization version GIF version |
Description: The affirmation of 𝜑 denies the denial of 𝜑. Identical to notnot 142. Axiom 41 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-frege41 | ⊢ (𝜑 → ¬ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . 2 wff 𝜑 | |
2 | 1 | wn 3 | . . 3 wff ¬ 𝜑 |
3 | 2 | wn 3 | . 2 wff ¬ ¬ 𝜑 |
4 | 1, 3 | wi 4 | 1 wff (𝜑 → ¬ ¬ 𝜑) |
Colors of variables: wff setvar class |
This axiom is referenced by: frege42 41413 |
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