nic-isw2 - New Foundations Explorer

	New Foundations Explorer		< Previous Next > Nearby theorems
Mirrors > Home > NFE Home > Th. List > nic-isw2		Unicode version

Theorem nic-isw2 1446

Description: Inference for swapping nested terms. (Contributed by Jeff Hoffman, 17-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

**Hypothesis**
Ref	Expression
nic-isw2.1	$-/\$ $-/\$

**Assertion**
Ref	Expression
nic-isw2	$-/\$ $-/\$

**Proof of Theorem nic-isw2**
Step	Hyp	Ref	Expression
1		nic-isw2.1	. . 3 $-/\$ $-/\$
2		nic-swap 1444	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
3	2	nic-imp 1440	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	1, 3	nic-mp 1436	. 2 $-/\$ $-/\$
5	4	nic-isw1 1445	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-bi1 1453 nic-bi2 1454 nic-luk1 1456 nic-luk2 1457

W3C validator