![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > pm3.1 | Structured version Visualization version GIF version |
Description: Theorem *3.1 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm3.1 | ⊢ ((𝜑 ∧ 𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anor 509 | . 2 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (¬ 𝜑 ∨ ¬ 𝜓)) | |
2 | 1 | biimpi 205 | 1 ⊢ ((𝜑 ∧ 𝜓) → ¬ (¬ 𝜑 ∨ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∧ wa 383 |
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 196 df-or 384 df-an 385 |
This theorem is referenced by: pm3.14 522 |
Copyright terms: Public domain | W3C validator |