Theorem 3mix1 1326

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 863	. 2 ⊢ (𝜑 → (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		3orass 1086	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	sylibr 236	1 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ wo 843   ∨ w3o 1082

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 209  df-or 844  df-3or 1084

This theorem is referenced by:  3mix2  1327  3mix3  1328  3mix1i  1329  3mix1d  1332  3jaob  1422  tppreqb  4740  onzsl  7563  sornom  9701  fpwwe2lem13  10066  nn0le2is012  12049  hashv01gt1  13708  hash1to3  13852  cshwshashlem1  16431  zabsle1  25874  colinearalg  26698  frgrregorufr0  28105  sltsolem1  33182  nosep1o  33188  frege129d  40115