3ioran - New Foundations Explorer

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Theorem 3ioran 950

Description: Negated triple disjunction as triple conjunction. (Contributed by Scott Fenton, 19-Apr-2011.)

**Assertion**
Ref	Expression
3ioran	$\/$ $\/$ $/\$ $/\$

**Proof of Theorem 3ioran**
Step	Hyp	Ref	Expression
1		ioran 476	. . 3 $\/$ $/\$
2	1	anbi1i 676	. 2 $\/$ $/\$ $/\$ $/\$
3		ioran 476	. . 3 $\/$ $\/$ $\/$ $/\$
4		df-3or 935	. . 3 $\/$ $\/$ $\/$ $\/$
5	3, 4	xchnxbir 300	. 2 $\/$ $\/$ $\/$ $/\$
6		df-3an 936	. 2 $/\$ $/\$ $/\$ $/\$
7	2, 5, 6	3bitr4i 268	1 $\/$ $\/$ $/\$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wb 176 $\/$ wo 357 $/\$ wa 358 $\/$ w3o 933 $/\$ w3a 934

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-or 359 df-an 360 df-3or 935 df-3an 936

This theorem is referenced by: 3oran 951 cadnot 1394