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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 441 | . 2 ⊢ ((𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 → 𝜓)) | |
2 | 1 | bicomi 214 | 1 ⊢ (¬ (𝜑 → 𝜓) ↔ (𝜑 ∧ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 196 ∧ wa 384 |
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 197 df-an 386 |
This theorem is referenced by: pm4.65 443 npss 3717 difin 3861 isf32lem2 9176 nmo 29325 bnj1253 31085 unblimceq0 32498 fphpd 37380 rp-fakenanass 37860 clsk1independent 38344 nabctnabc 41098 islindeps 42242 |
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