3ioran - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > 3ioran		Unicode version

Theorem 3ioran 983

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 742	. . 3 $\/$ $/\$
2	1	anbi1i 454	. 2 $\/$ $/\$ $/\$ $/\$
3		ioran 742	. . 3 $\/$ $\/$ $\/$ $/\$
4		df-3or 969	. . 3 $\/$ $\/$ $\/$ $\/$
5	3, 4	xchnxbir 671	. 2 $\/$ $\/$ $\/$ $/\$
6		df-3an 970	. 2 $/\$ $/\$ $/\$ $/\$
7	2, 5, 6	3bitr4i 211	1 $\/$ $\/$ $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 103

wb 104 $\/$ wo 698 $\/$ w3o 967 $/\$ w3a 968

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 604 ax-in2 605 ax-io 699

This theorem depends on definitions: df-bi 116 df-3or 969 df-3an 970

This theorem is referenced by: ne3anior 2424 onntri35 7193