Theorem 3mix1 1332

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

Ref	Expression
3mix1	⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))

Proof of Theorem 3mix1

Step	Hyp	Ref	Expression
1		orc 868	. 2 ⊢ (𝜑 → (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		3orass 1090	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	sylibr 234	1 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 848   ∨ w3o 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-or 849  df-3or 1088

This theorem is referenced by:  3mix2  1333  3mix3  1334  3mix1i  1335  3mix1d  1338  3jaobOLD  1430  tppreqb  4750  onzsl  7797  sornom  10199  fpwwe2lem12  10565  nn0le2is012  12593  hashv01gt1  14307  hash1to3  14454  cshwshashlem1  17066  zabsle1  27259  nogesgn1o  27637  ltssolem1  27639  nosep1o  27645  colinearalg  28979  frgrregorufr0  30394  frege129d  44190