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Definition df-cad 1608
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 1609 and cadan 1610 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 1607 . 2 wff cadd(𝜑, 𝜓, 𝜒)
51, 2wa 396 . . 3 wff (𝜑𝜓)
61, 2wxo 1509 . . . 4 wff (𝜑𝜓)
73, 6wa 396 . . 3 wff (𝜒 ∧ (𝜑𝜓))
85, 7wo 845 . 2 wff ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓)))
94, 8wb 205 1 wff (cadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))
Colors of variables: wff setvar class
This definition is referenced by:  cador  1609  cadbi123d  1611  cadcoma  1613  cad11  1617  cad0  1619  cad0OLD  1620
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