nic-swap - Metamath Proof Explorer

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Theorem nic-swap 1604

Description: The connector $-/\$ is symmetric. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

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

**Proof of Theorem nic-swap**
Step	Hyp	Ref	Expression
1		nic-id 1603	. 2 $-/\$ $-/\$
2		nic-ax 1598	. 2 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
3	1, 2	nic-mp 1596	1 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$

Colors of variables: wff setvar class

Syntax hints: $-/\$ 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-an 386 df-nan 1448

This theorem is referenced by: nic-isw1 1605 nic-isw2 1606 nic-bijust 1612 nic-luk1 1616

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