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Theorem nic-mp 1445
 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 1447. 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 1300 . . . 4
42, 3mpbi 200 . . 3
54simprd 450 . 2
61, 5ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wnan 1296 This theorem is referenced by:  nic-imp  1449  nic-idlem2  1451  nic-id  1452  nic-swap  1453  nic-isw1  1454  nic-isw2  1455  nic-iimp1  1456  nic-idel  1458  nic-ich  1459  nic-stdmp  1464  nic-luk1  1465  nic-luk2  1466  nic-luk3  1467  lukshefth1  1469  lukshefth2  1470  renicax  1471 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 178  df-an 361  df-nan 1297
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