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Definition df-cad 1609
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 1610 and cadan 1611 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 1608 . 2 wff cadd(𝜑, 𝜓, 𝜒)
51, 2wa 399 . . 3 wff (𝜑𝜓)
61, 2wxo 1502 . . . 4 wff (𝜑𝜓)
73, 6wa 399 . . 3 wff (𝜒 ∧ (𝜑𝜓))
85, 7wo 844 . 2 wff ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓)))
94, 8wb 209 1 wff (cadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))
Colors of variables: wff setvar class
This definition is referenced by:  cador  1610  cadbi123d  1612  cadcoma  1614  cad0  1619  cad11  1621
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