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Theorem aibnbna 41073
Description: Given a implies b, (not b), there exists a proof for (not a). (Contributed by Jarvin Udandy, 1-Sep-2016.)
Hypotheses
Ref Expression
aibnbna.1  |-  ( ph  ->  ps )
aibnbna.2  |-  -.  ps
Assertion
Ref Expression
aibnbna  |-  -.  ph

Proof of Theorem aibnbna
StepHypRef Expression
1 aibnbna.2 . 2  |-  -.  ps
2 aibnbna.1 . 2  |-  ( ph  ->  ps )
31, 2mto 188 1  |-  -.  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  aibnbaif  41074
  Copyright terms: Public domain W3C validator