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Theorem nic-swap 1245
Description: -/\ is symmetric. (Contributed by Jeff Hoffman, 17-Nov-2007.)
Assertion
Ref Expression
nic-swap |- ((th -/\ ph) -/\ ((ph -/\ th) -/\ (ph -/\ th)))

Proof of Theorem nic-swap
StepHypRef Expression
1 nic-id 1244 . 2 |- (ph -/\ (ph -/\ ph))
2 nic-ax 1239 . 2 |- ((ph -/\ (ph -/\ ph)) -/\ ((ta -/\ (ta -/\ ta)) -/\ ((th -/\ ph) -/\ ((ph -/\ th) -/\ (ph -/\ th)))))
31, 2nic-mp 1237 1 |- ((th -/\ ph) -/\ ((ph -/\ th) -/\ (ph -/\ th)))
Colors of variables: wff set class
Syntax hints:   -/\ wnand 1229
This theorem is referenced by:  nic-isw1 1246  nic-isw2 1247  nic-luk1 1257
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7
This theorem depends on definitions:  df-bi 164  df-an 242  df-nand 1230
Copyright terms: Public domain