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Theorem cnf2dd 29062
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnf2dd.1  |-  ( ph  ->  ( ps  ->  -.  th ) )
cnf2dd.2  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
Assertion
Ref Expression
cnf2dd  |-  ( ph  ->  ( ps  ->  ch ) )

Proof of Theorem cnf2dd
StepHypRef Expression
1 cnf2dd.1 . 2  |-  ( ph  ->  ( ps  ->  -.  th ) )
2 cnf2dd.2 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  \/  th ) ) )
32orcomdd 29060 . 2  |-  ( ph  ->  ( ps  ->  ( th  \/  ch ) ) )
41, 3cnf1dd 29061 1  |-  ( ph  ->  ( ps  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368
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 370  df-an 371
This theorem is referenced by:  cnfn2dd  29064  mpt2bi123f  29143  mptbi12f  29147  ac6s6  29152
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