3ioran - Intuitionistic Logic Explorer

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Theorem 3ioran 993

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 752	. . 3 $\/$ $/\$
2	1	anbi1i 458	. 2 $\/$ $/\$ $/\$ $/\$
3		ioran 752	. . 3 $\/$ $\/$ $\/$ $/\$
4		df-3or 979	. . 3 $\/$ $\/$ $\/$ $\/$
5	3, 4	xchnxbir 681	. 2 $\/$ $\/$ $\/$ $/\$
6		df-3an 980	. 2 $/\$ $/\$ $/\$ $/\$
7	2, 5, 6	3bitr4i 212	1 $\/$ $\/$ $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 104

wb 105 $\/$ wo 708 $\/$ w3o 977 $/\$ w3a 978

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709

This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980

This theorem is referenced by: ne3anior 2433 onntri35 7226