nic-bi2 - New Foundations Explorer

	New Foundations Explorer		< Previous Next > Nearby theorems
Mirrors > Home > NFE Home > Th. List > nic-bi2		Unicode version

Theorem nic-bi2 1454

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 1446	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
3		nic-id 1443	. . 3 $-/\$ $-/\$
4	2, 3	nic-iimp1 1447	. 2 $-/\$ $-/\$
5	4	nic-idel 1449	1 $-/\$ $-/\$

Colors of variables: wff setvar class

Syntax hints: $-/\$ wnan 1287

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 177 df-an 360 df-nan 1288

This theorem is referenced by: nic-stdmp 1455 nic-luk1 1456 nic-luk2 1457 nic-luk3 1458

W3C validator