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	⊢ ((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 1001	. 2 wff (𝜑 ∨ 𝜓 ∨ 𝜒)
5	1, 2	wo 713	. . 3 wff (𝜑 ∨ 𝜓)
6	5, 3	wo 713	. 2 wff ((𝜑 ∨ 𝜓) ∨ 𝜒)
7	4, 6	wb 105	1 wff ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))

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  6647  nntri1  6650  nnsseleq  6655  elznn0nn  9468  zleloe  9501  uzm1  9761  xrnemnf  9981  xrnepnf  9982  xrltso  10000  hashfiv01gt1  11012  swrdnd  11199  prm23ge5  12795  bd3or  16216  triap  16427