Theorem 3mix1 1331

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 866	. 2 ⊢ (𝜑 → (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		3orass 1091	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	sylibr 233	1 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 846   ∨ w3o 1087

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 206  df-or 847  df-3or 1089

This theorem is referenced by:  3mix2  1332  3mix3  1333  3mix1i  1334  3mix1d  1337  3jaob  1427  tppreqb  4809  onzsl  7835  sornom  10272  fpwwe2lem12  10637  nn0le2is012  12626  hashv01gt1  14305  hash1to3  14452  cshwshashlem1  17029  zabsle1  26799  nogesgn1o  27176  sltsolem1  27178  nosep1o  27184  colinearalg  28168  frgrregorufr0  29577  frege129d  42514