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Theorem cnfn1dd 31774
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnfn1dd.1  |-  ( ph  ->  ( ps  ->  ch ) )
cnfn1dd.2  |-  ( ph  ->  ( ps  ->  ( -.  ch  \/  th )
) )
Assertion
Ref Expression
cnfn1dd  |-  ( ph  ->  ( ps  ->  th )
)

Proof of Theorem cnfn1dd
StepHypRef Expression
1 cnfn1dd.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
2 notnot1 122 . . 3  |-  ( ch 
->  -.  -.  ch )
31, 2syl6 31 . 2  |-  ( ph  ->  ( ps  ->  -.  -.  ch ) )
4 cnfn1dd.2 . 2  |-  ( ph  ->  ( ps  ->  ( -.  ch  \/  th )
) )
53, 4cnf1dd 31772 1  |-  ( ph  ->  ( ps  ->  th )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 366
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:  mpt2bi123f  31853  mptbi12f  31857  ac6s6  31862
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