Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > pm2.45 | Structured version Visualization version GIF version |
Description: Theorem *2.45 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.45 | ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 864 | . 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓)) | |
2 | 1 | con3i 154 | 1 ⊢ (¬ (𝜑 ∨ 𝜓) → ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ 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-or 845 |
This theorem is referenced by: pm2.47 881 dn1 1055 eueq3 3650 outpasch 27112 acopyeu 27191 tgasa1 27215 unbdqndv2lem1 34683 |
Copyright terms: Public domain | W3C validator |