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Theorem nic-bi2 1614

Description: Inference to extract the other side of an implication from a 'biconditional' definition. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

**Hypothesis**
Ref	Expression
nic-bi2.1	$-/\$ $-/\$ $-/\$ $-/\$ $-/\$

**Assertion**
Ref	Expression
nic-bi2	$-/\$ $-/\$

**Proof of Theorem nic-bi2**
Step	Hyp	Ref	Expression
1		nic-bi2.1	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
2	1	nic-isw2 1606	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
3		nic-id 1603	. . 3 $-/\$ $-/\$
4	2, 3	nic-iimp1 1607	. 2 $-/\$ $-/\$
5	4	nic-idel 1609	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-stdmp 1615 nic-luk1 1616 nic-luk2 1617 nic-luk3 1618

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