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Theorem nic-bi2 1463
Description: Inference to extract the other side of an implication from a 'biconditional' definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-bi2.1  |-  ( (
ph  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ps  -/\  ps )
) )
Assertion
Ref Expression
nic-bi2  |-  ( ps 
-/\  ( ph  -/\  ph )
)

Proof of Theorem nic-bi2
StepHypRef Expression
1 nic-bi2.1 . . . 4  |-  ( (
ph  -/\  ps )  -/\  ( ( ph  -/\  ph )  -/\  ( ps  -/\  ps )
) )
21nic-isw2 1455 . . 3  |-  ( (
ph  -/\  ps )  -/\  ( ( ps  -/\  ps )  -/\  ( ph  -/\  ph ) ) )
3 nic-id 1452 . . 3  |-  ( ps 
-/\  ( ps  -/\  ps ) )
42, 3nic-iimp1 1456 . 2  |-  ( ps 
-/\  ( ph  -/\  ps )
)
54nic-idel 1458 1  |-  ( ps 
-/\  ( ph  -/\  ph )
)
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1296
This theorem is referenced by:  nic-stdmp  1464  nic-luk1  1465  nic-luk2  1466  nic-luk3  1467
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 1297
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