Definition df-3or 1003

Description: Define disjunction ('or') of 3 wff's. Definition *2.33 of [WhiteheadRussell] p. 105. This abbreviation reduces the number of parentheses and emphasizes that the order of bracketing is not important by virtue of the associative law orass 772. (Contributed by NM, 8-Apr-1994.)

Assertion

Ref	Expression
df-3or	|- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )

Detailed syntax breakdown of Definition df-3or

Step	Hyp	Ref	Expression
1		wph	. . 3 wff ph
2		wps	. . 3 wff ps
3		wch	. . 3 wff ch
4	1, 2, 3	w3o 1001	. 2 wff ( ph \/ ps \/ ch )
5	1, 2	wo 713	. . 3 wff ( ph \/ ps )
6	5, 3	wo 713	. 2 wff ( ( ph \/ ps ) \/ ch )
7	4, 6	wb 105	1 wff ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )

This definition is referenced by:  3orass  1005  3orrot  1008  3ioran  1017  3orbi123i  1213  3ori  1334  3jao  1335  mpjao3dan  1341  3orbi123d  1345  3orim123d  1354  3or6  1357  ecase23d  1384  hb3or  1595  eueq3dc  2977  eltpg  3711  rextpg  3720  nntri3or  6639  nntri1  6642  nnsseleq  6647  elznn0nn  9460  zleloe  9493  uzm1  9753  xrnemnf  9973  xrnepnf  9974  xrltso  9992  hashfiv01gt1  11004  swrdnd  11191  prm23ge5  12787  bd3or  16192  triap  16397