Theorem 3mix2d 1338

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 1332	. 2 ⊢ (𝜓 → (𝜒 ∨ 𝜓 ∨ 𝜃))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜒 ∨ 𝜓 ∨ 𝜃))

Syntax hints:   → wi 4   ∨ 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:  sosn  5741  f1dom3fv3dif  7261  f1dom3el3dif  7262  xpord3inddlem  8153  elfiun  9442  fpwwe2lem12  10656  fvf1tp  13806  swrdnd0  14675  lcmfunsnlem2lem2  16658  dyaddisjlem  25548  sltsolem1  27639  tgcolg  28533  btwncolg2  28535  hlln  28586  btwnlng2  28599  frgrregorufr0  30305  constrsslem  33775  constrlccllem  33787  colineartriv2  36086  gpgprismgriedgdmss  48056  gpgvtxedg0  48067  gpgvtxedg1  48068  eenglngeehlnmlem2  48718