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Theorem nic-imp 1483
Description: Inference for nic-mp 1479 using nic-ax 1481 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 1481 . 2  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  -/\  (
( ta  -/\  ( ta  -/\  ta ) ) 
-/\  ( ( th 
-/\  ch )  -/\  (
( ph  -/\  th )  -/\  ( ph  -/\  th )
) ) ) )
31, 2nic-mp 1479 1  |-  ( ( th  -/\  ch )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) )
Colors of variables: wff setvar class
Syntax hints:    -/\ wnan 1334
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 185  df-an 371  df-nan 1335
This theorem is referenced by:  nic-idlem1  1484  nic-idlem2  1485  nic-isw2  1489  nic-iimp1  1490  nic-idel  1492  nic-ich  1493  nic-idbl  1494  nic-luk1  1499
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