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Theorem nic-idbl 1441
Description: Double the terms. Since doubling is the same as negation, this can be viewed as a contraposition inference. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-idbl.1  |-  ( ph  -/\  ( ps  -/\  ps )
)
Assertion
Ref Expression
nic-idbl  |-  ( ( ps  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ph  -/\  ph )
) )

Proof of Theorem nic-idbl
StepHypRef Expression
1 nic-idbl.1 . . 3  |-  ( ph  -/\  ( ps  -/\  ps )
)
21nic-imp 1430 . 2  |-  ( ( ps  -/\  ps )  -/\  ( ( ph  -/\  ps )  -/\  ( ph  -/\  ps )
) )
31nic-imp 1430 . 2  |-  ( (
ph  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ph  -/\  ph )
) )
42, 3nic-ich 1440 1  |-  ( ( ps  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ph  -/\  ph )
) )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1287
This theorem is referenced by:  nic-luk1  1446
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 177  df-an 360  df-nan 1288
  Copyright terms: Public domain W3C validator