nic-dfneg - Metamath Proof Explorer

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Theorem nic-dfneg 1595

Description: Define negation 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-dfneg	$-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$

**Proof of Theorem nic-dfneg**
Step	Hyp	Ref	Expression
1		nannot 1453	. . 3 $-/\$
2	1	bicomi 214	. 2 $-/\$
3		nanbi 1454	. 2 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	2, 3	mpbi 220	1 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wb 196 $-/\$ 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-or 385 df-an 386 df-nan 1448

This theorem is referenced by: nic-luk2 1617 nic-luk3 1618

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