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| Mirrors > Home > MPE Home > Th. List > df-3or | Structured version Visualization version GIF version | ||
| Description: Define disjunction ('or') of three wff's. Definition *2.33 of [WhiteheadRussell] p. 105. This abbreviation reduces the number of parentheses and emphasizes that the order of bracketing is not important by virtue of the associative law orass 922. (Contributed by NM, 8-Apr-1994.) |
| Ref | Expression |
|---|---|
| df-3or | ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph | . . 3 wff 𝜑 | |
| 2 | wps | . . 3 wff 𝜓 | |
| 3 | wch | . . 3 wff 𝜒 | |
| 4 | 1, 2, 3 | w3o 1086 | . 2 wff (𝜑 ∨ 𝜓 ∨ 𝜒) |
| 5 | 1, 2 | wo 848 | . . 3 wff (𝜑 ∨ 𝜓) |
| 6 | 5, 3 | wo 848 | . 2 wff ((𝜑 ∨ 𝜓) ∨ 𝜒) |
| 7 | 4, 6 | wb 206 | 1 wff ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒)) |
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