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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 404 | . 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓)) | |
2 | 1 | bicomi 223 | 1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 205 ∧ wa 396 |
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 397 |
This theorem is referenced by: pm4.65 406 npss 4045 difin 4195 2nreu 4375 isf32lem2 10110 cat1 17812 nmo 30838 hashxpe 31127 bnj1253 32997 fphpd 40638 clsk1independent 41656 nabctnabc 44426 islindeps 45794 |
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