Definition df-3or 981

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 768. (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 979	. 2 wff (𝜑 ∨ 𝜓 ∨ 𝜒)
5	1, 2	wo 709	. . 3 wff (𝜑 ∨ 𝜓)
6	5, 3	wo 709	. 2 wff ((𝜑 ∨ 𝜓) ∨ 𝜒)
7	4, 6	wb 105	1 wff ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))

This definition is referenced by:  3orass  983  3orrot  986  3ioran  995  3orbi123i  1191  3ori  1311  3jao  1312  mpjao3dan  1318  3orbi123d  1322  3orim123d  1331  3or6  1334  ecase23d  1361  hb3or  1560  eueq3dc  2934  eltpg  3663  rextpg  3672  nntri3or  6546  nntri1  6549  nnsseleq  6554  elznn0nn  9331  zleloe  9364  uzm1  9623  xrnemnf  9843  xrnepnf  9844  xrltso  9862  hashfiv01gt1  10853  prm23ge5  12402  bd3or  15321  triap  15519