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  6629  nntri1  6632  nnsseleq  6637  elznn0nn  9448  zleloe  9481  uzm1  9741  xrnemnf  9961  xrnepnf  9962  xrltso  9980  hashfiv01gt1  10991  swrdnd  11177  prm23ge5  12773  bd3or  16122  triap  16328