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Mirrors > Home > MPE Home > Th. List > nic-mp | Structured version Visualization version Unicode version |
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 1598. 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.) |
Ref | Expression |
---|---|
nic-jmin | |
nic-jmaj |
Ref | Expression |
---|---|
nic-mp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nic-jmin | . 2 | |
2 | nic-jmaj | . . . 4 | |
3 | nannan 1451 | . . . 4 | |
4 | 2, 3 | mpbi 220 | . . 3 |
5 | 4 | simprd 479 | . 2 |
6 | 1, 5 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wnan 1447 |
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 197 df-an 386 df-nan 1448 |
This theorem is referenced by: nic-imp 1600 nic-idlem2 1602 nic-id 1603 nic-swap 1604 nic-isw1 1605 nic-isw2 1606 nic-iimp1 1607 nic-idel 1609 nic-ich 1610 nic-stdmp 1615 nic-luk1 1616 nic-luk2 1617 nic-luk3 1618 lukshefth1 1620 lukshefth2 1621 renicax 1622 |
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