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Theorem nanim 1386
Description: Show equivalence between implication and the Nicod version. To derive nic-dfim 1546, apply nanbi 1388. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nanim  |-  ( (
ph  ->  ps )  <->  ( ph  -/\  ( ps  -/\  ps )
) )

Proof of Theorem nanim
StepHypRef Expression
1 nannan 1384 . 2  |-  ( (
ph  -/\  ( ps  -/\  ps ) )  <->  ( ph  ->  ( ps  /\  ps ) ) )
2 anidmdbi 650 . 2  |-  ( (
ph  ->  ( ps  /\  ps ) )  <->  ( ph  ->  ps ) )
31, 2bitr2i 253 1  |-  ( (
ph  ->  ps )  <->  ( ph  -/\  ( ps  -/\  ps )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ wa 370    -/\ wnan 1379
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-nan 1380
This theorem is referenced by:  nic-dfim  1546  nic-ax  1550  waj-ax  31016  lukshef-ax2  31017
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