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Theorem inegd 1279
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 112 . 2  |-  ( ph  ->  ( ps  -> F.  ) )
3 dfnot 1278 . 2  |-  ( -. 
ps 
<->  ( ps  -> F.  ) )
42, 3sylibr 141 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 101   F. wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  genpdisj  6679  cauappcvgprlemdisj  6807  caucvgprlemdisj  6830  caucvgprprlemdisj  6858  resqrexlemgt0  9847  resqrexlemoverl  9848  leabs  9901  climge0  10076
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