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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 | pm4.56 985 | . 2 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓)) | |
2 | 1 | con2bii 360 | 1 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 208 ∧ wa 398 ∨ wo 843 |
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 209 df-an 399 df-or 844 |
This theorem is referenced by: pm4.57 987 norassOLD 1530 19.43OLD 1880 ordthauslem 21985 mideulem2 26514 opphllem 26515 ordtconnlem1 31162 poimirlem9 34895 ftc1anclem1 34961 xrlttri5d 41542 |
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