nic-luk3 - Metamath Proof Explorer

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Theorem nic-luk3 1259

Description: Proof of luk-3 1217 from nic-ax 1239 and nic-mp 1237. (Contributed by Jeff Hoffman, 18-Nov-2007.)

**Assertion**
Ref	Expression
nic-luk3

**Proof of Theorem nic-luk3**
Step	Hyp	Ref	Expression
1		nic-dfim 1235	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
2	1	nic-bi1 1254	. . 3 $-/\$ $-/\$ $-/\$ $-/\$
3		nic-dfneg 1236	. . . . 5 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	3	nic-bi2 1255	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$
5		nic-id 1244	. . . 4 $-/\$ $-/\$
6	4, 5	nic-iimp1 1248	. . 3 $-/\$
7	2, 6	nic-iimp2 1249	. 2 $-/\$ $-/\$
8		nic-dfim 1235	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
9	8	nic-bi1 1254	. 2 $-/\$ $-/\$ $-/\$ $-/\$
10	7, 9	nic-mp 1237	1

Colors of variables: wff set class

Syntax hints:

wn 2

wi 3 $-/\$ wnand 1229

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