nic-isw2 - Metamath Proof Explorer

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Theorem nic-isw2 1247

Description: Inference for swapping nested terms. (Contributed by Jeff Hoffman, 17-Nov-2007.)

**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 1245	. . . 4 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
3	2	nic-imp 1241	. . 3 $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$ $-/\$
4	1, 3	nic-mp 1237	. 2 $-/\$ $-/\$
5	4	nic-isw1 1246	1 $-/\$ $-/\$

Colors of variables: wff set class

Syntax hints: $-/\$ wnand 1229

This theorem is referenced by: nic-bi1 1254 nic-bi2 1255 nic-luk1 1257 nic-luk2 1258

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