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Theorem nic-mp 1504
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 1506. 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 1348 . . . 4
42, 3mpbi 208 . . 3
54simprd 463 . 2
61, 5ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  -/\wnan 1343
This theorem is referenced by:  nic-imp  1508  nic-idlem2  1510  nic-id  1511  nic-swap  1512  nic-isw1  1513  nic-isw2  1514  nic-iimp1  1515  nic-idel  1517  nic-ich  1518  nic-stdmp  1523  nic-luk1  1524  nic-luk2  1525  nic-luk3  1526  lukshefth1  1528  lukshefth2  1529  renicax  1530
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-nan 1344
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