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Theorem nic-isw2 1456
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 1454 . . . 4  |-  ( (
ph  -/\  th )  -/\  ( ( th  -/\  ph )  -/\  ( th  -/\  ph )
) )
32nic-imp 1450 . . 3  |-  ( ( ps  -/\  ( th  -/\  ph ) )  -/\  (
( ( ph  -/\  th )  -/\  ps )  -/\  (
( ph  -/\  th )  -/\  ps ) ) )
41, 3nic-mp 1446 . 2  |-  ( (
ph  -/\  th )  -/\  ps )
54nic-isw1 1455 1  |-  ( ps 
-/\  ( ph  -/\  th )
)
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1297
This theorem is referenced by:  nic-bi1  1463  nic-bi2  1464  nic-luk1  1466  nic-luk2  1467
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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