nic-idlem2 - Metamath Proof Explorer

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Theorem nic-idlem2 1243

Description: Lemma for nic-id 1244. Inference used by nic-id 1244.

**Hypothesis**
Ref	Expression
nic-idlem2.1	$-/\$ $-/\$ $-/\$ $-/\$

**Assertion**
Ref	Expression
nic-idlem2	$-/\$ $-/\$ $-/\$ $-/\$

**Proof of Theorem nic-idlem2**
Step	Hyp	Ref	Expression
1		nic-idlem2.1	. 2 $-/\$ $-/\$ $-/\$ $-/\$
2		nic-ax 1239	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
3	2	nic-imp 1241	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	3	nic-imp 1241	. 2 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
5	1, 4	nic-mp 1237	1 $-/\$ $-/\$ $-/\$ $-/\$

Colors of variables: wff set class

Syntax hints: $-/\$ wnand 1229

This theorem is referenced by: nic-id 1244

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-an 242 df-nand 1230