3ioran - Intuitionistic Logic Explorer

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Theorem 3ioran 988

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 747	. . 3 $\/$ $/\$
2	1	anbi1i 455	. 2 $\/$ $/\$ $/\$ $/\$
3		ioran 747	. . 3 $\/$ $\/$ $\/$ $/\$
4		df-3or 974	. . 3 $\/$ $\/$ $\/$ $\/$
5	3, 4	xchnxbir 676	. 2 $\/$ $\/$ $\/$ $/\$
6		df-3an 975	. 2 $/\$ $/\$ $/\$ $/\$
7	2, 5, 6	3bitr4i 211	1 $\/$ $\/$ $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 103

wb 104 $\/$ wo 703 $\/$ w3o 972 $/\$ w3a 973

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704

This theorem depends on definitions: df-bi 116 df-3or 974 df-3an 975

This theorem is referenced by: ne3anior 2428 onntri35 7214