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Theorem nic-swap 1434
Description:  -/\ is symmetric. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-swap  |-  ( ( th  -/\  ph )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) )

Proof of Theorem nic-swap
StepHypRef Expression
1 nic-id 1433 . 2  |-  ( ph  -/\  ( ph  -/\  ph )
)
2 nic-ax 1428 . 2  |-  ( (
ph  -/\  ( ph  -/\  ph )
)  -/\  ( ( ta  -/\  ( ta  -/\  ta ) )  -/\  (
( th  -/\  ph )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) ) ) )
31, 2nic-mp 1426 1  |-  ( ( th  -/\  ph )  -/\  ( ( ph  -/\  th )  -/\  ( ph  -/\  th )
) )
Colors of variables: wff set class
Syntax hints:    -/\ wnan 1287
This theorem is referenced by:  nic-isw1  1435  nic-isw2  1436  nic-bijust  1442  nic-luk1  1446
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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