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 867	. 2 ⊢ (𝜑 → (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		3orass 1089	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	sylibr 234	1 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 847   ∨ w3o 1085

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 848  df-3or 1087

This theorem is referenced by:  3mix2  1332  3mix3  1333  3mix1i  1334  3mix1d  1337  3jaobOLD  1429  tppreqb  4754  onzsl  7776  sornom  10168  fpwwe2lem12  10533  nn0le2is012  12537  hashv01gt1  14252  hash1to3  14399  cshwshashlem1  17007  zabsle1  27234  nogesgn1o  27612  sltsolem1  27614  nosep1o  27620  colinearalg  28888  frgrregorufr0  30304  frege129d  43866