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Mirrors > Home > MPE Home > Th. List > pm4.43 | Structured version Visualization version GIF version |
Description: Theorem *4.43 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 26-Nov-2012.) |
Ref | Expression |
---|---|
pm4.43 | ⊢ (𝜑 ↔ ((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ ¬ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.24 403 | . . 3 ⊢ ¬ (𝜓 ∧ ¬ 𝜓) | |
2 | 1 | biorfi 936 | . 2 ⊢ (𝜑 ↔ (𝜑 ∨ (𝜓 ∧ ¬ 𝜓))) |
3 | ordi 1003 | . 2 ⊢ ((𝜑 ∨ (𝜓 ∧ ¬ 𝜓)) ↔ ((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ ¬ 𝜓))) | |
4 | 2, 3 | bitri 274 | 1 ⊢ (𝜑 ↔ ((𝜑 ∨ 𝜓) ∧ (𝜑 ∨ ¬ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∧ wa 396 ∨ wo 844 |
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 845 |
This theorem is referenced by: stoweidlem26 43526 |
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