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Theorem atnaiana 38230
Description: Given a, it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020.)
Hypothesis
Ref Expression
atnaiana.1  |-  ph
Assertion
Ref Expression
atnaiana  |-  -.  ( ph  ->  ( ph  /\  -.  ph ) )

Proof of Theorem atnaiana
StepHypRef Expression
1 atnaiana.1 . . . 4  |-  ph
21bitru 1450 . . 3  |-  ( ph  <-> T.  )
3 pm3.24 891 . . . 4  |-  -.  ( ph  /\  -.  ph )
43bifal 1451 . . 3  |-  ( (
ph  /\  -.  ph )  <-> F.  )
52, 4aifftbifffaibif 38228 . 2  |-  ( (
ph  ->  ( ph  /\  -.  ph ) )  <-> F.  )
65aisfina 38204 1  |-  -.  ( ph  ->  ( ph  /\  -.  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 371
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 189  df-an 373  df-tru 1441  df-fal 1444
This theorem is referenced by:  ainaiaandna  38231  confun5  38250
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