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Definition df-cad 1599
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 1600 and cadan 1601 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 1598 . 2 wff cadd(𝜑, 𝜓, 𝜒)
51, 2wa 396 . . 3 wff (𝜑𝜓)
61, 2wxo 1495 . . . 4 wff (𝜑𝜓)
73, 6wa 396 . . 3 wff (𝜒 ∧ (𝜑𝜓))
85, 7wo 841 . 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  1600  cadbi123d  1602  cadcoma  1604  cad0  1609  cad11  1611
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