Definition df-3or 1005

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 774. (Contributed by NM, 8-Apr-1994.)

Assertion

Ref	Expression
df-3or	⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))

Detailed syntax breakdown of Definition df-3or

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		wps	. . 3 wff 𝜓
3		wch	. . 3 wff 𝜒
4	1, 2, 3	w3o 1003	. 2 wff (𝜑 ∨ 𝜓 ∨ 𝜒)
5	1, 2	wo 715	. . 3 wff (𝜑 ∨ 𝜓)
6	5, 3	wo 715	. 2 wff ((𝜑 ∨ 𝜓) ∨ 𝜒)
7	4, 6	wb 105	1 wff ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))

This definition is referenced by:  3orass  1007  3orrot  1010  3ioran  1019  3orbi123i  1215  3ori  1336  3jao  1337  mpjao3dan  1343  3orbi123d  1347  3orim123d  1356  3or6  1359  ecase23d  1386  hb3or  1597  eueq3dc  2980  eltpg  3714  rextpg  3723  nntri3or  6660  nntri1  6663  nnsseleq  6668  elznn0nn  9492  zleloe  9525  uzm1  9786  xrnemnf  10011  xrnepnf  10012  xrltso  10030  hashfiv01gt1  11043  swrdnd  11239  prm23ge5  12836  bd3or  16424  triap  16633