3ioran - Intuitionistic Logic Explorer

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Theorem 3ioran 934

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 701	. . 3 $\/$ $/\$
2	1	anbi1i 445	. 2 $\/$ $/\$ $/\$ $/\$
3		ioran 701	. . 3 $\/$ $\/$ $\/$ $/\$
4		df-3or 920	. . 3 $\/$ $\/$ $\/$ $\/$
5	3, 4	xchnxbir 638	. 2 $\/$ $\/$ $\/$ $/\$
6		df-3an 921	. 2 $/\$ $/\$ $/\$ $/\$
7	2, 5, 6	3bitr4i 210	1 $\/$ $\/$ $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 102

wb 103 $\/$ wo 661 $\/$ w3o 918 $/\$ w3a 919

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662

This theorem depends on definitions: df-bi 115 df-3or 920 df-3an 921

This theorem is referenced by: ne3anior 2333