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Definition df-cad 1693
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 1694 and cadan 1695 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 1692 . 2 wff cadd(𝜑, 𝜓, 𝜒)
51, 2wa 382 . . 3 wff (𝜑𝜓)
61, 2wxo 1611 . . . 4 wff (𝜑𝜓)
73, 6wa 382 . . 3 wff (𝜒 ∧ (𝜑𝜓))
85, 7wo 826 . 2 wff ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓)))
94, 8wb 196 1 wff (cadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))
Colors of variables: wff setvar class
This definition is referenced by:  cador  1694  cadbi123d  1696  cadcoma  1698  cad0  1703  cad11  1705
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