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Theorem 3mix1 1331
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3mix1 (𝜑 → (𝜑𝜓𝜒))

Proof of Theorem 3mix1
StepHypRef Expression
1 orc 866 . 2 (𝜑 → (𝜑 ∨ (𝜓𝜒)))
2 3orass 1091 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
31, 2sylibr 237 1 (𝜑 → (𝜑𝜓𝜒))
Colors of variables: wff setvar class
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 210  df-or 847  df-3or 1089
This theorem is referenced by:  3mix2  1332  3mix3  1333  3mix1i  1334  3mix1d  1337  3jaob  1427  tppreqb  4693  onzsl  7580  sornom  9777  fpwwe2lem12  10142  nn0le2is012  12127  hashv01gt1  13797  hash1to3  13943  cshwshashlem1  16532  zabsle1  26032  colinearalg  26856  frgrregorufr0  28261  nogesgn1o  33517  sltsolem1  33519  nosep1o  33525  frege129d  40917
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