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Theorem cad0 1400
Description: If one parameter is false, the adder carry is true exactly when both of the other two parameters are true. (Contributed by Mario Carneiro, 8-Sep-2016.)
Assertion
Ref Expression
cad0 cadd

Proof of Theorem cad0
StepHypRef Expression
1 df-cad 1381 . 2 cadd  \/_
2 idd 21 . . . 4
3 pm2.21 100 . . . . 5
43adantrd 454 . . . 4  \/_
52, 4jaod 369 . . 3  \/_
6 orc 374 . . 3  \/_
75, 6impbid1 194 . 2  \/_
81, 7syl5bb 248 1 cadd
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wo 357   wa 358    \/_ wxo 1304  caddwcad 1379
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 177  df-or 359  df-an 360  df-cad 1381
This theorem is referenced by: (None)
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