nic-dfim - Metamath Proof Explorer

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Theorem nic-dfim 1235

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).

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

**Proof of Theorem nic-dfim**
Step	Hyp	Ref	Expression
1		nic-justim 1232	. . 3 $-/\$ $-/\$
2	1	bicomi 189	. 2 $-/\$ $-/\$
3		nic-justbi 1234	. 2 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	2, 3	mpbi 206	1 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$

Colors of variables: wff set class

Syntax hints:

wi 3

wb 163 $-/\$ wnand 1229

This theorem is referenced by: nic-stdmp 1256 nic-luk1 1257 nic-luk2 1258 nic-luk3 1259

This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7

This theorem depends on definitions: df-bi 164 df-or 241 df-an 242 df-nand 1230