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Theorem cnf1dd 30730
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnf1dd.1  |-  ( ph  ->  ( ps  ->  -.  ch ) )
cnf1dd.2  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
Assertion
Ref Expression
cnf1dd  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem cnf1dd
StepHypRef Expression
1 cnf1dd.1 . . 3  |-  ( ph  ->  ( ps  ->  -.  ch ) )
2 cnf1dd.2 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
31, 2jcad 531 . 2  |-  ( ph  ->  ( ps  ->  ( -.  ch  /\  ( ch  \/  th ) ) ) )
4 df-or 368 . . 3  |-  ( ( ch  \/  th )  <->  ( -.  ch  ->  th )
)
5 pm3.35 585 . . 3  |-  ( ( -.  ch  /\  ( -.  ch  ->  th )
)  ->  th )
64, 5sylan2b 473 . 2  |-  ( ( -.  ch  /\  ( ch  \/  th ) )  ->  th )
73, 6syl6 33 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 366    /\ wa 367
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 185  df-or 368  df-an 369
This theorem is referenced by:  cnf2dd  30731  cnfn1dd  30732  mpt2bi123f  30811  mptbi12f  30815  ac6s6  30820
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