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Theorem nic-id 1244
Description: Theorem id 73 expressed with -/\. (Contributed by Jeff Hoffman, 17-Nov-2007.)
Assertion
Ref Expression
nic-id |- (ta -/\ (ta -/\ ta))

Proof of Theorem nic-id
StepHypRef Expression
1 nic-ax 1239 . . 3 |- ((ps -/\ (ps -/\ ps)) -/\ ((th -/\ (th -/\ th)) -/\ ((ph -/\ ps) -/\ ((ps -/\ ph) -/\ (ps -/\ ph)))))
21nic-idlem2 1243 . 2 |- ((((ph -/\ ps) -/\ ((ps -/\ ph) -/\ (ps -/\ ph))) -/\ (ch -/\ (ch -/\ ch))) -/\ (ps -/\ (ps -/\ ps)))
3 nic-idlem1 1242 . . 3 |- (((ch -/\ (ch -/\ ch)) -/\ (ta -/\ (ta -/\ ta))) -/\ ((((ph -/\ ps) -/\ ((ps -/\ ph) -/\ (ps -/\ ph))) -/\ (ch -/\ (ch -/\ ch))) -/\ (((ph -/\ ps) -/\ ((ps -/\ ph) -/\ (ps -/\ ph))) -/\ (ch -/\ (ch -/\ ch)))))
43nic-idlem2 1243 . 2 |- (((((ph -/\ ps) -/\ ((ps -/\ ph) -/\ (ps -/\ ph))) -/\ (ch -/\ (ch -/\ ch))) -/\ (ps -/\ (ps -/\ ps))) -/\ ((ch -/\ (ch -/\ ch)) -/\ (ta -/\ (ta -/\ ta))))
52, 4nic-mp 1237 1 |- (ta -/\ (ta -/\ ta))
Colors of variables: wff set class
Syntax hints:   -/\ wnand 1229
This theorem is referenced by:  nic-swap 1245  nic-idel 1250  nic-bijust 1253  nic-bi1 1254  nic-bi2 1255  nic-luk2 1258  nic-luk3 1259
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