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Theorem nic-imp 1435
Description: Inference for nic-mp 1431 using nic-ax 1433 as major premise. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-imp.1  |-  ( ph  -/\  ( ch  -/\  ps )
)
Assertion
Ref Expression
nic-imp  |-  ( ( th  -/\  ch )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) )

Proof of Theorem nic-imp
StepHypRef Expression
1 nic-imp.1 . 2  |-  ( ph  -/\  ( ch  -/\  ps )
)
2 nic-ax 1433 . 2  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  -/\  (
( ta  -/\  ( ta  -/\  ta ) ) 
-/\  ( ( th 
-/\  ch )  -/\  (
( ph  -/\  th )  -/\  ( ph  -/\  th )
) ) ) )
31, 2nic-mp 1431 1  |-  ( ( th  -/\  ch )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1292
This theorem is referenced by:  nic-idlem1  1436  nic-idlem2  1437  nic-isw2  1441  nic-iimp1  1442  nic-idel  1444  nic-ich  1445  nic-idbl  1446  nic-luk1  1451
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362  df-nan 1293
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