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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-vd3 | Structured version Visualization version GIF version |
Description: Definition of a 3-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-vd3 | ⊢ (( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | wps | . . 3 wff 𝜓 | |
3 | wch | . . 3 wff 𝜒 | |
4 | wth | . . 3 wff 𝜃 | |
5 | 1, 2, 3, 4 | wvd3 41908 | . 2 wff ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
6 | 1, 2, 3 | w3a 1089 | . . 3 wff (𝜑 ∧ 𝜓 ∧ 𝜒) |
7 | 6, 4 | wi 4 | . 2 wff ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
8 | 5, 7 | wb 209 | 1 wff (( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) ↔ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)) |
Colors of variables: wff setvar class |
This definition is referenced by: dfvd3 41912 |
Copyright terms: Public domain | W3C validator |