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Mirrors > Home > MPE Home > Th. List > pm3.13 | Structured version Visualization version GIF version |
Description: Theorem *3.13 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm3.13 | ⊢ (¬ (𝜑 ∧ 𝜓) → (¬ 𝜑 ∨ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.11 989 | . 2 ⊢ (¬ (¬ 𝜑 ∨ ¬ 𝜓) → (𝜑 ∧ 𝜓)) | |
2 | 1 | con1i 147 | 1 ⊢ (¬ (𝜑 ∧ 𝜓) → (¬ 𝜑 ∨ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 395 ∨ 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 206 df-an 396 df-or 844 |
This theorem is referenced by: ifcomnan 4512 suc11 6354 nn0xmulclb 30996 naim1 34505 naim2 34506 tsbi1 36218 vk15.4j 42037 vk15.4jVD 42423 |
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