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Theorem atbiffatnnb 27848
Description: If a implies b, then a implies not not b (Contributed by Jarvin Udandy, 28-Aug-2016.)
Assertion
Ref Expression
atbiffatnnb  |-  ( (
ph  ->  ps )  -> 
( ph  ->  -.  -.  ps ) )

Proof of Theorem atbiffatnnb
StepHypRef Expression
1 idd 22 . . 3  |-  ( ph  ->  ( ps  ->  ps ) )
2 notnot 283 . . 3  |-  ( ps  <->  -. 
-.  ps )
31, 2syl6ib 218 . 2  |-  ( ph  ->  ( ps  ->  -.  -.  ps ) )
43a2i 13 1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  -.  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  atbiffatnnbalt  27850
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 178
  Copyright terms: Public domain W3C validator