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Theorem nic-mp 1436
 Description: Derive Nicod's rule of modus ponens using 'nand', from the standard one. Although the major and minor premise together also imply , this form is necessary for useful derivations from nic-ax 1438. In a pure (standalone) treatment of Nicod's axiom, this theorem would be changed to an axiom (\$a statement). (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-jmin
nic-jmaj
Assertion
Ref Expression
nic-mp

Proof of Theorem nic-mp
StepHypRef Expression
1 nic-jmin . 2
2 nic-jmaj . . . 4
3 nannan 1291 . . . 4
42, 3mpbi 199 . . 3
54simprd 449 . 2
61, 5ax-mp 8 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   wnan 1287 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 This theorem is referenced by:  nic-imp  1440  nic-idlem2  1442  nic-id  1443  nic-swap  1444  nic-isw1  1445  nic-isw2  1446  nic-iimp1  1447  nic-idel  1449  nic-ich  1450  nic-stdmp  1455  nic-luk1  1456  nic-luk2  1457  nic-luk3  1458  lukshefth1  1460  lukshefth2  1461  renicax  1462
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