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Theorem cad11 1409
Description: If two parameters are true, the adder carry is true. (Contributed by Mario Carneiro, 4-Sep-2016.)
Assertion
Ref Expression
cad11  |-  ( (
ph  /\  ps )  -> cadd ( ph ,  ps ,  ch ) )

Proof of Theorem cad11
StepHypRef Expression
1 orc 376 . 2  |-  ( (
ph  /\  ps )  ->  ( ( ph  /\  ps )  \/  ( ch  /\  ( ph  \/_  ps ) ) ) )
2 df-cad 1391 . 2  |-  (cadd (
ph ,  ps ,  ch )  <->  ( ( ph  /\ 
ps )  \/  ( ch  /\  ( ph  \/_  ps ) ) ) )
31, 2sylibr 205 1  |-  ( (
ph  /\  ps )  -> cadd ( ph ,  ps ,  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 359    /\ wa 360    \/_ wxo 1314  caddwcad 1389
This theorem is referenced by:  cadtru  1411
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 179  df-or 361  df-cad 1391
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