3anor - Metamath Proof Explorer

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Theorem 3anor 989

Description: Triple conjunction expressed in terms of triple disjunction. (Contributed by Jeff Hankins, 15-Aug-2009.)

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

**Proof of Theorem 3anor**
Step	Hyp	Ref	Expression
1		df-3an 975	. 2 $/\$ $/\$ $/\$ $/\$
2		anor 489	. . . 4 $/\$ $/\$ $/\$ $\/$
3		ianor 488	. . . . 5 $/\$ $\/$
4	3	orbi1i 520	. . . 4 $/\$ $\/$ $\/$ $\/$
5	2, 4	xchbinx 310	. . 3 $/\$ $/\$ $\/$ $\/$
6		df-3or 974	. . 3 $\/$ $\/$ $\/$ $\/$
7	5, 6	xchbinxr 311	. 2 $/\$ $/\$ $\/$ $\/$
8	1, 7	bitri 249	1 $/\$ $/\$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wb 184 $\/$ wo 368 $/\$ wa 369 $\/$ w3o 972 $/\$ w3a 973

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 185 df-or 370 df-an 371 df-3or 974 df-3an 975

This theorem is referenced by: 3ianor 990 ne3anior 2793