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 845  df-3or 1085

This theorem is referenced by:  sosn  5755  f1dom3fv3dif  7262  f1dom3el3dif  7263  xpord3inddlem  8137  elfiun  9424  fpwwe2lem12  10636  swrdnd0  14611  lcmfunsnlem2lem2  16581  dyaddisjlem  25475  sltsolem1  27559  tgcolg  28309  btwncolg2  28311  hlln  28362  btwnlng2  28375  frgrregorufr0  30082  colineartriv2  35573  eenglngeehlnmlem2  47680