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Theorem nic-mp 1548
 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 1550. 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 1384 . . . 4
42, 3mpbi 211 . . 3
54simprd 464 . 2
61, 5ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wnan 1379 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 188  df-an 372  df-nan 1380 This theorem is referenced by:  nic-imp  1552  nic-idlem2  1554  nic-id  1555  nic-swap  1556  nic-isw1  1557  nic-isw2  1558  nic-iimp1  1559  nic-idel  1561  nic-ich  1562  nic-stdmp  1567  nic-luk1  1568  nic-luk2  1569  nic-luk3  1570  lukshefth1  1572  lukshefth2  1573  renicax  1574
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