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Mirrors > Home > NFE Home > Th. List > nic-mp | 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 ![]() |
Ref | Expression |
---|---|
nic-jmin |
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nic-jmaj |
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Ref | Expression |
---|---|
nic-mp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nic-jmin |
. 2
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2 | nic-jmaj |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | nannan 1291 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | mpbi 199 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 4 | simprd 449 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
6 | 1, 5 | ax-mp 5 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
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 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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