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Mirrors > Home > MPE Home > Th. List > pm5.63 | Structured version Visualization version GIF version |
Description: Theorem *5.63 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 25-Dec-2012.) |
Ref | Expression |
---|---|
pm5.63 | ⊢ ((𝜑 ∨ 𝜓) ↔ (𝜑 ∨ (¬ 𝜑 ∧ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmid 895 | . . 3 ⊢ (𝜑 ∨ ¬ 𝜑) | |
2 | ordi 1006 | . . 3 ⊢ ((𝜑 ∨ (¬ 𝜑 ∧ 𝜓)) ↔ ((𝜑 ∨ ¬ 𝜑) ∧ (𝜑 ∨ 𝜓))) | |
3 | 1, 2 | mpbiran 709 | . 2 ⊢ ((𝜑 ∨ (¬ 𝜑 ∧ 𝜓)) ↔ (𝜑 ∨ 𝜓)) |
4 | 3 | bicomi 227 | 1 ⊢ ((𝜑 ∨ 𝜓) ↔ (𝜑 ∨ (¬ 𝜑 ∧ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ∧ wa 399 ∨ wo 847 |
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 df-or 848 |
This theorem is referenced by: jaoi2 1060 plydivex 25214 lineunray 34212 wl-df4-3mintru2 35421 |
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