Theorem 3ioran 991

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 490	. . 3
2	1	anbi1i 695	. 2
3		ioran 490	. . 3
4		df-3or 974	. . 3
5	3, 4	xchnxbir 309	. 2
6		df-3an 975	. 2
7	2, 5, 6	3bitr4i 277	1

Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  \/w3o 972  /\w3a 973

This theorem is referenced by:  3oran  992  cadnot  1461  fbunfip  20370  wwlknndef  24737  wwlknfi  24738  clwwlknndef  24773  frgraregord013  25118  wl-nfeqfb  29990

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 185  df-or 370  df-an 371  df-3or 974  df-3an 975