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Definition df-cad 1590
Description: Definition of the "carry" output of the full adder. It is true when at least two arguments are true, so it is equal to the "majority" function on three variables. See cador 1591 and cadan 1592 for alternate definitions. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
df-cad (cadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))

Detailed syntax breakdown of Definition df-cad
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 wps . . 3 wff 𝜓
3 wch . . 3 wff 𝜒
41, 2, 3wcad 1589 . 2 wff cadd(𝜑, 𝜓, 𝜒)
51, 2wa 396 . . 3 wff (𝜑𝜓)
61, 2wxo 1496 . . . 4 wff (𝜑𝜓)
73, 6wa 396 . . 3 wff (𝜒 ∧ (𝜑𝜓))
85, 7wo 842 . 2 wff ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓)))
94, 8wb 207 1 wff (cadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))
Colors of variables: wff setvar class
This definition is referenced by:  cador  1591  cadbi123d  1593  cadcoma  1595  cad0  1600  cad11  1602
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