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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-frege28 | Structured version Visualization version GIF version |
Description: Contraposition. Identical to con3 153. Theorem *2.16 of [WhiteheadRussell] p. 103. Axiom 28 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-frege28 | ⊢ ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . 2 wff 𝜑 | |
2 | wps | . 2 wff 𝜓 | |
3 | 2 | wn 3 | . . 3 wff ¬ 𝜓 |
4 | 1 | wn 3 | . . 3 wff ¬ 𝜑 |
5 | 3, 4 | wi 4 | . 2 wff (¬ 𝜓 → ¬ 𝜑) |
6 | 1, 2, 5 | bj-0 34716 | 1 wff ((𝜑 → 𝜓) → (¬ 𝜓 → ¬ 𝜑)) |
Colors of variables: wff setvar class |
This axiom is referenced by: frege29 41407 frege33 41412 frege54cor0a 41439 |
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