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Theorem nic-id 1448
Description: Theorem id 19 expressed with  -/\. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-id  |-  ( ta 
-/\  ( ta  -/\  ta ) )

Proof of Theorem nic-id
StepHypRef Expression
1 nic-ax 1443 . . 3  |-  ( ( ps  -/\  ( ps  -/\ 
ps ) )  -/\  ( ( th  -/\  ( th  -/\  th ) ) 
-/\  ( ( ph  -/\ 
ps )  -/\  (
( ps  -/\  ph )  -/\  ( ps  -/\  ph )
) ) ) )
21nic-idlem2 1447 . 2  |-  ( ( ( ( ph  -/\  ps )  -/\  ( ( ps  -/\  ph )  -/\  ( ps  -/\  ph ) ) )  -/\  ( ch  -/\  ( ch 
-/\  ch ) ) ) 
-/\  ( ps  -/\  ( ps  -/\  ps )
) )
3 nic-idlem1 1446 . . 3  |-  ( ( ( ch  -/\  ( ch  -/\  ch ) ) 
-/\  ( ta  -/\  ( ta  -/\  ta )
) )  -/\  (
( ( ( ph  -/\ 
ps )  -/\  (
( ps  -/\  ph )  -/\  ( ps  -/\  ph )
) )  -/\  ( ch  -/\  ( ch  -/\  ch ) ) )  -/\  ( ( ( ph  -/\ 
ps )  -/\  (
( ps  -/\  ph )  -/\  ( ps  -/\  ph )
) )  -/\  ( ch  -/\  ( ch  -/\  ch ) ) ) ) )
43nic-idlem2 1447 . 2  |-  ( ( ( ( ( ph  -/\ 
ps )  -/\  (
( ps  -/\  ph )  -/\  ( ps  -/\  ph )
) )  -/\  ( ch  -/\  ( ch  -/\  ch ) ) )  -/\  ( ps  -/\  ( ps 
-/\  ps ) ) ) 
-/\  ( ( ch 
-/\  ( ch  -/\  ch ) )  -/\  ( ta  -/\  ( ta  -/\  ta ) ) ) )
52, 4nic-mp 1441 1  |-  ( ta 
-/\  ( ta  -/\  ta ) )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1292
This theorem is referenced by:  nic-swap  1449  nic-idel  1454  nic-bi1  1458  nic-bi2  1459  nic-luk2  1462  nic-luk3  1463
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 1293
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