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Theorem inegd 1308
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 113 . 2  |-  ( ph  ->  ( ps  -> F.  ) )
3 dfnot 1307 . 2  |-  ( -. 
ps 
<->  ( ps  -> F.  ) )
42, 3sylibr 132 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102   F. wfal 1294
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295
This theorem is referenced by:  genpdisj  7082  cauappcvgprlemdisj  7210  caucvgprlemdisj  7233  caucvgprprlemdisj  7261  resqrexlemgt0  10453  resqrexlemoverl  10454  leabs  10507  climge0  10713
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