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Mirrors > Home > MPE Home > Th. List > pm3.14 | Structured version Visualization version GIF version |
Description: Theorem *3.14 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm3.14 | ⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.1 988 | . 2 ⊢ ((𝜑 ∧ 𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓)) | |
2 | 1 | con2i 139 | 1 ⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 395 ∨ wo 844 |
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 206 df-an 396 df-or 845 |
This theorem is referenced by: naim1 35775 naim2 35776 finxpreclem2 36772 tsan2 37514 tsan3 37515 ntrneiel2 43387 onenotinotbothi 46189 twonotinotbothi 46190 |
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