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Definition df-3nand 32520
Description: The double nand. This definition allows us to express the input of three variables only being false if all three are true. (Contributed by Anthony Hart, 2-Sep-2011.)
Assertion
Ref Expression
df-3nand ((𝜑𝜓𝜒) ↔ (𝜑 → (𝜓 → ¬ 𝜒)))

Detailed syntax breakdown of Definition df-3nand
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 wps . . 3 wff 𝜓
3 wch . . 3 wff 𝜒
41, 2, 3w3nand 32519 . 2 wff (𝜑𝜓𝜒)
53wn 3 . . . 4 wff ¬ 𝜒
62, 5wi 4 . . 3 wff (𝜓 → ¬ 𝜒)
71, 6wi 4 . 2 wff (𝜑 → (𝜓 → ¬ 𝜒))
84, 7wb 196 1 wff ((𝜑𝜓𝜒) ↔ (𝜑 → (𝜓 → ¬ 𝜒)))
Colors of variables: wff setvar class
This definition is referenced by:  df3nandALT1  32521  df3nandALT2  32522  andnand1  32523
  Copyright terms: Public domain W3C validator