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Theorem inegd 1323
Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
inegd.1  |-  ( (
ph  /\  ps )  ->  F.  )
Assertion
Ref Expression
inegd  |-  ( ph  ->  -.  ps )

Proof of Theorem inegd
StepHypRef Expression
1 inegd.1 . . 3  |-  ( (
ph  /\  ps )  ->  F.  )
21ex 423 . 2  |-  ( ph  ->  ( ps  ->  F.  ) )
3 dfnot 1322 . 2  |-  ( -. 
ps 
<->  ( ps  ->  F.  ) )
42, 3sylibr 203 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358    F. wfal 1308
This theorem is referenced by:  efald  1324
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-an 360  df-tru 1310  df-fal 1311
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