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Mirrors > Home > MPE Home > Th. List > oran | Structured version Visualization version GIF version |
Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.) |
Ref | Expression |
---|---|
oran | ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.56 987 | . 2 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓)) | |
2 | 1 | con2bii 357 | 1 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∧ wa 396 ∨ wo 845 |
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 df-or 846 |
This theorem is referenced by: pm4.57 989 19.43OLD 1886 ordthauslem 22878 mideulem2 27974 opphllem 27975 ordtconnlem1 32892 poimirlem9 36485 ftc1anclem1 36549 onsucf1olem 42005 xrlttri5d 43979 |
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