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Mirrors > Home > MPE Home > Th. List > con1 | Structured version Visualization version GIF version |
Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102. Its associated inference is con1i 147. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 12-Feb-2013.) |
Ref | Expression |
---|---|
con1 | ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜑 → 𝜓)) | |
2 | 1 | con1d 145 | 1 ⊢ ((¬ 𝜑 → 𝜓) → (¬ 𝜓 → 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: con1b 359 nneob 8478 uzwo 12662 |
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