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Theorem nic-bi1 1443
Description: Inference to extract one side of an implication from a definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-bi1.1  |-  ( (
ph  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ps  -/\  ps )
) )
Assertion
Ref Expression
nic-bi1  |-  ( ph  -/\  ( ps  -/\  ps )
)

Proof of Theorem nic-bi1
StepHypRef Expression
1 nic-bi1.1 . . . 4  |-  ( (
ph  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ps  -/\  ps )
) )
2 nic-id 1433 . . . 4  |-  ( ph  -/\  ( ph  -/\  ph )
)
31, 2nic-iimp1 1437 . . 3  |-  ( ph  -/\  ( ph  -/\  ps )
)
43nic-isw2 1436 . 2  |-  ( ph  -/\  ( ps  -/\  ph )
)
54nic-idel 1439 1  |-  ( ph  -/\  ( ps  -/\  ps )
)
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1287
This theorem is referenced by:  nic-luk1  1446  nic-luk2  1447  nic-luk3  1448
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
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