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Theorem nic-id 1433
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 1428 . . 3  |-  ( ( ps  -/\  ( ps  -/\ 
ps ) )  -/\  ( ( th  -/\  ( th  -/\  th ) ) 
-/\  ( ( ph  -/\ 
ps )  -/\  (
( ps  -/\  ph )  -/\  ( ps  -/\  ph )
) ) ) )
21nic-idlem2 1432 . 2  |-  ( ( ( ( ph  -/\  ps )  -/\  ( ( ps  -/\  ph )  -/\  ( ps  -/\  ph ) ) )  -/\  ( ch  -/\  ( ch 
-/\  ch ) ) ) 
-/\  ( ps  -/\  ( ps  -/\  ps )
) )
3 nic-idlem1 1431 . . 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 1432 . 2  |-  ( ( ( ( ( ph  -/\ 
ps )  -/\  (
( ps  -/\  ph )  -/\  ( ps  -/\  ph )
) )  -/\  ( ch  -/\  ( ch  -/\  ch ) ) )  -/\  ( ps  -/\  ( ps 
-/\  ps ) ) ) 
-/\  ( ( ch 
-/\  ( ch  -/\  ch ) )  -/\  ( ta  -/\  ( ta  -/\  ta ) ) ) )
52, 4nic-mp 1426 1  |-  ( ta 
-/\  ( ta  -/\  ta ) )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1287
This theorem is referenced by:  nic-swap  1434  nic-idel  1439  nic-bi1  1443  nic-bi2  1444  nic-luk2  1447  nic-luk3  1448
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
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