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Theorem nic-idlem2 1432
Description: Lemma for nic-id 1433. Inference used by nic-id 1433. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-idlem2.1  |-  ( et 
-/\  ( ( ph  -/\  ( ch  -/\  ps )
)  -/\  th )
)
Assertion
Ref Expression
nic-idlem2  |-  ( ( th  -/\  ( ta  -/\  ( ta  -/\  ta )
) )  -/\  et )

Proof of Theorem nic-idlem2
StepHypRef Expression
1 nic-idlem2.1 . 2  |-  ( et 
-/\  ( ( ph  -/\  ( ch  -/\  ps )
)  -/\  th )
)
2 nic-ax 1428 . . . 4  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  -/\  (
( ta  -/\  ( ta  -/\  ta ) ) 
-/\  ( ( ph  -/\ 
ch )  -/\  (
( ph  -/\  ph )  -/\  ( ph  -/\  ph )
) ) ) )
32nic-imp 1430 . . 3  |-  ( ( th  -/\  ( ta  -/\  ( ta  -/\  ta )
) )  -/\  (
( ( ph  -/\  ( ch  -/\  ps ) ) 
-/\  th )  -/\  (
( ph  -/\  ( ch 
-/\  ps ) )  -/\  th ) ) )
43nic-imp 1430 . 2  |-  ( ( et  -/\  ( ( ph  -/\  ( ch  -/\  ps ) )  -/\  th )
)  -/\  ( (
( th  -/\  ( ta  -/\  ( ta  -/\  ta ) ) )  -/\  et )  -/\  ( ( th  -/\  ( ta  -/\  ( ta  -/\  ta )
) )  -/\  et ) ) )
51, 4nic-mp 1426 1  |-  ( ( th  -/\  ( ta  -/\  ( ta  -/\  ta )
) )  -/\  et )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1287
This theorem is referenced by:  nic-id  1433
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