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Theorem nic-isw2 1436
Description: Inference for swapping nested terms. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nic-isw2.1  |-  ( ps 
-/\  ( th  -/\  ph )
)
Assertion
Ref Expression
nic-isw2  |-  ( ps 
-/\  ( ph  -/\  th )
)

Proof of Theorem nic-isw2
StepHypRef Expression
1 nic-isw2.1 . . 3  |-  ( ps 
-/\  ( th  -/\  ph )
)
2 nic-swap 1434 . . . 4  |-  ( (
ph  -/\  th )  -/\  ( ( th  -/\  ph )  -/\  ( th  -/\  ph )
) )
32nic-imp 1430 . . 3  |-  ( ( ps  -/\  ( th  -/\  ph ) )  -/\  (
( ( ph  -/\  th )  -/\  ps )  -/\  (
( ph  -/\  th )  -/\  ps ) ) )
41, 3nic-mp 1426 . 2  |-  ( (
ph  -/\  th )  -/\  ps )
54nic-isw1 1435 1  |-  ( ps 
-/\  ( ph  -/\  th )
)
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1287
This theorem is referenced by:  nic-bi1  1443  nic-bi2  1444  nic-luk1  1446  nic-luk2  1447
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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