3anor - Metamath Proof Explorer

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Theorem 3anor 1001

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 987	. 2 $/\$ $/\$ $/\$ $/\$
2		anor 492	. . . 4 $/\$ $/\$ $/\$ $\/$
3		ianor 491	. . . . 5 $/\$ $\/$
4	3	orbi1i 523	. . . 4 $/\$ $\/$ $\/$ $\/$
5	2, 4	xchbinx 312	. . 3 $/\$ $/\$ $\/$ $\/$
6		df-3or 986	. . 3 $\/$ $\/$ $\/$ $\/$
7	5, 6	xchbinxr 313	. 2 $/\$ $/\$ $\/$ $\/$
8	1, 7	bitri 253	1 $/\$ $/\$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wb 188 $\/$ wo 370 $/\$ wa 371 $\/$ w3o 984 $/\$ w3a 985

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 189 df-or 372 df-an 373 df-3or 986 df-3an 987

This theorem is referenced by: 3ianor 1002 ne3anior 2717