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Theorem cad11 1556
Description: If (at least) two inputs are true, then the adder carry is true. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
cad11 ((𝜑𝜓) → cadd(𝜑, 𝜓, 𝜒))

Proof of Theorem cad11
StepHypRef Expression
1 orc 400 . 2 ((𝜑𝜓) → ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))
2 df-cad 1544 . 2 (cadd(𝜑, 𝜓, 𝜒) ↔ ((𝜑𝜓) ∨ (𝜒 ∧ (𝜑𝜓))))
31, 2sylibr 224 1 ((𝜑𝜓) → cadd(𝜑, 𝜓, 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 383  wa 384  wxo 1462  caddwcad 1543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-or 385  df-cad 1544
This theorem is referenced by:  cadtru  1557
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