Theorem 3mix2d 1334

Description: Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011.)

Hypothesis

Ref	Expression
3mixd.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3mix2d	⊢ (𝜑 → (𝜒 ∨ 𝜓 ∨ 𝜃))

Proof of Theorem 3mix2d

Step	Hyp	Ref	Expression
1		3mixd.1	. 2 ⊢ (𝜑 → 𝜓)
2		3mix2 1328	. 2 ⊢ (𝜓 → (𝜒 ∨ 𝜓 ∨ 𝜃))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜒 ∨ 𝜓 ∨ 𝜃))

Syntax hints:   → wi 4   ∨ w3o 1083

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 846  df-3or 1085

This theorem is referenced by:  sosn  5766  f1dom3fv3dif  7282  f1dom3el3dif  7283  xpord3inddlem  8163  elfiun  9459  fpwwe2lem12  10671  swrdnd0  14645  lcmfunsnlem2lem2  16615  dyaddisjlem  25542  sltsolem1  27626  tgcolg  28376  btwncolg2  28378  hlln  28429  btwnlng2  28442  frgrregorufr0  30152  colineartriv2  35669  eenglngeehlnmlem2  47862