Users' Mathboxes Mathbox for Giovanni Mascellani < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  cnfn2dd Structured version   Unicode version

Theorem cnfn2dd 29036
Description: A lemma for Conjunctive Normal Form unit propagation, in double deduction form. (Contributed by Giovanni Mascellani, 19-Mar-2018.)
Hypotheses
Ref Expression
cnfn2dd.1  |-  ( ph  ->  ( ps  ->  th )
)
cnfn2dd.2  |-  ( ph  ->  ( ps  ->  ( ch  \/  -.  th )
) )
Assertion
Ref Expression
cnfn2dd  |-  ( ph  ->  ( ps  ->  ch ) )

Proof of Theorem cnfn2dd
StepHypRef Expression
1 cnfn2dd.1 . . 3  |-  ( ph  ->  ( ps  ->  th )
)
2 notnot1 122 . . 3  |-  ( th 
->  -.  -.  th )
31, 2syl6 33 . 2  |-  ( ph  ->  ( ps  ->  -.  -.  th ) )
4 cnfn2dd.2 . 2  |-  ( ph  ->  ( ps  ->  ( ch  \/  -.  th )
) )
53, 4cnf2dd 29034 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:  mpt2bi123f  29115  mptbi12f  29119  ac6s6  29124
  Copyright terms: Public domain W3C validator