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Theorem nic-iimp1 1457
Description: Inference version of nic-imp 1450 using right-handed term. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-iimp1.1  |-  ( ph  -/\  ( ch  -/\  ps )
)
nic-iimp1.2  |-  ( th 
-/\  ch )
Assertion
Ref Expression
nic-iimp1  |-  ( th 
-/\  ph )

Proof of Theorem nic-iimp1
StepHypRef Expression
1 nic-iimp1.2 . . 3  |-  ( th 
-/\  ch )
2 nic-iimp1.1 . . . 4  |-  ( ph  -/\  ( ch  -/\  ps )
)
32nic-imp 1450 . . 3  |-  ( ( th  -/\  ch )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) )
41, 3nic-mp 1446 . 2  |-  ( ph  -/\ 
th )
54nic-isw1 1455 1  |-  ( th 
-/\  ph )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1297
This theorem is referenced by:  nic-iimp2  1458  nic-bi1  1463  nic-bi2  1464  nic-luk2  1467  nic-luk3  1468
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 179  df-an 362  df-nan 1298
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