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Theorem nic-dfim 1434

Description: Define implication in terms of 'nand'. Analogous to

$-/\$

. In a pure (standalone) treatment of Nicod's axiom, this theorem would be changed to a definition ($a statement). (Contributed by NM, 11-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
nic-dfim	$-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$

**Proof of Theorem nic-dfim**
Step	Hyp	Ref	Expression
1		nanim 1292	. . 3 $-/\$ $-/\$
2	1	bicomi 193	. 2 $-/\$ $-/\$
3		nanbi 1294	. 2 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	2, 3	mpbi 199	1 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 176 $-/\$ wnan 1287

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-or 359 df-an 360 df-nan 1288

This theorem is referenced by: nic-stdmp 1455 nic-luk1 1456 nic-luk2 1457 nic-luk3 1458

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