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Definition df-cad 1543
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 1544 and cadan 1545 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 1542 . 2 wff cadd(𝜑, 𝜓, 𝜒)
51, 2wa 384 . . 3 wff (𝜑𝜓)
61, 2wxo 1461 . . . 4 wff (𝜑𝜓)
73, 6wa 384 . . 3 wff (𝜒 ∧ (𝜑𝜓))
85, 7wo 383 . 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  1544  cadbi123d  1546  cadcoma  1548  cad0  1553  cad11  1555
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