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| Mirrors > Home > MPE Home > Th. List > pm4.61 | Structured version Visualization version GIF version | ||
| Description: Theorem *4.61 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) |
| Ref | Expression |
|---|---|
| pm4.61 | ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | annim 403 | . 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓)) | |
| 2 | 1 | bicomi 224 | 1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓)) |
| Colors of variables: wff setvar class |
| Syntax hints: ¬ wn 3 → wi 4 ↔ wb 206 ∧ wa 395 |
| 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 207 df-an 396 |
| This theorem is referenced by: pm4.65 405 npss 4113 difin 4272 2nreu 4444 isf32lem2 10394 cat1 18142 nmo 32509 hashxpe 32811 bnj1253 35031 fphpd 42827 clsk1independent 44059 nabctnabc 46943 islindeps 48370 |
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