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Theorem cad11 1389
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 374 . 2  |-  ( (
ph  /\  ps )  ->  ( ( ph  /\  ps )  \/  ( ch  /\  ( ph \/_ ps ) ) ) )
2 df-cad 1371 . 2  |-  (cadd (
ph ,  ps ,  ch )  <->  ( ( ph  /\ 
ps )  \/  ( ch  /\  ( ph \/_ ps ) ) ) )
31, 2sylibr 203 1  |-  ( (
ph  /\  ps )  -> cadd ( ph ,  ps ,  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358   \/_wxo 1295  caddwcad 1369
This theorem is referenced by:  cadtru  1391
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-cad 1371
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