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Theorem ainaiaandna 38383
Description: Given a, a implies it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020.)
Hypothesis
Ref Expression
ainaiaandna.1  |-  ph
Assertion
Ref Expression
ainaiaandna  |-  ( ph  ->  -.  ( ph  ->  (
ph  /\  -.  ph )
) )

Proof of Theorem ainaiaandna
StepHypRef Expression
1 ainaiaandna.1 . . 3  |-  ph
21atnaiana 38382 . 2  |-  -.  ( ph  ->  ( ph  /\  -.  ph ) )
32a1i 11 1  |-  ( ph  ->  -.  ( ph  ->  (
ph  /\  -.  ph )
) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 370
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 188  df-an 372  df-tru 1440  df-fal 1443
This theorem is referenced by: (None)
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