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Mirrors > Home > MPE Home > Th. List > pm4.44 | Structured version Visualization version GIF version |
Description: Theorem *4.44 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.44 | ⊢ (𝜑 ↔ (𝜑 ∨ (𝜑 ∧ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 864 | . 2 ⊢ (𝜑 → (𝜑 ∨ (𝜑 ∧ 𝜓))) | |
2 | id 22 | . . 3 ⊢ (𝜑 → 𝜑) | |
3 | simpl 483 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜑) | |
4 | 2, 3 | jaoi 854 | . 2 ⊢ ((𝜑 ∨ (𝜑 ∧ 𝜓)) → 𝜑) |
5 | 1, 4 | impbii 208 | 1 ⊢ (𝜑 ↔ (𝜑 ∨ (𝜑 ∧ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ 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: (None) |
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