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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 141 | 1 ⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 398 ∨ wo 843 |
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 209 df-an 399 df-or 844 |
This theorem is referenced by: naim1 33741 naim2 33742 finxpreclem2 34675 tsan2 35424 tsan3 35425 ntrneiel2 40442 onenotinotbothi 43176 twonotinotbothi 43177 |
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