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Theorem nic-idel 1455
Description: Inference to remove the trailing term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-idel.1  |-  ( ph  -/\  ( ch  -/\  ps )
)
Assertion
Ref Expression
nic-idel  |-  ( ph  -/\  ( ch  -/\  ch )
)

Proof of Theorem nic-idel
StepHypRef Expression
1 nic-id 1449 . . 3  |-  ( ch 
-/\  ( ch  -/\  ch ) )
21nic-isw1 1451 . 2  |-  ( ( ch  -/\  ch )  -/\  ch )
3 nic-idel.1 . . 3  |-  ( ph  -/\  ( ch  -/\  ps )
)
43nic-imp 1446 . 2  |-  ( ( ( ch  -/\  ch )  -/\  ch )  -/\  (
( ph  -/\  ( ch 
-/\  ch ) )  -/\  ( ph  -/\  ( ch  -/\ 
ch ) ) ) )
52, 4nic-mp 1442 1  |-  ( ph  -/\  ( ch  -/\  ch )
)
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1293
This theorem is referenced by:  nic-bi1  1459  nic-bi2  1460  nic-luk1  1462
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 178  df-an 361  df-nan 1294
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