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Theorem nanim 1301
Description: Show equivalence between implication and the Nicod version. To derive nic-dfim 1443, apply nanbi 1303. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nanim  |-  ( (
ph  ->  ps )  <->  ( ph  -/\  ( ps  -/\  ps )
) )

Proof of Theorem nanim
StepHypRef Expression
1 nannan 1300 . 2  |-  ( (
ph  -/\  ( ps  -/\  ps ) )  <->  ( ph  ->  ( ps  /\  ps ) ) )
2 anidmdbi 628 . 2  |-  ( (
ph  ->  ( ps  /\  ps ) )  <->  ( ph  ->  ps ) )
31, 2bitr2i 242 1  |-  ( (
ph  ->  ps )  <->  ( ph  -/\  ( ps  -/\  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359    -/\ wnan 1296
This theorem is referenced by:  nic-dfim  1443  nic-ax  1447  waj-ax  26156  lukshef-ax2  26157
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  df-an 361  df-nan 1297
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