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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 407 | . 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓)) | |
2 | 1 | bicomi 227 | 1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 209 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: pm4.65 409 npss 4011 difin 4162 2nreu 4341 isf32lem2 9867 cat1 17482 nmo 30425 hashxpe 30715 bnj1253 32581 fphpd 40251 clsk1independent 41243 nabctnabc 44006 islindeps 45376 |
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