Theorem 3mix1d 1337

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

Hypothesis

Ref	Expression
3mixd.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3mix1d	⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜃))

Proof of Theorem 3mix1d

Step	Hyp	Ref	Expression
1		3mixd.1	. 2 ⊢ (𝜑 → 𝜓)
2		3mix1 1331	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜒 ∨ 𝜃))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 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:  f1dom3fv3dif  7225  f1dom3el3dif  7226  xpord3inddlem  8110  elfiun  9357  prinfzo0  13635  fvf1tp  13727  lcmfunsnlem2lem2  16585  estrreslem2  18075  ostth  27526  noextendlt  27557  sltsolem1  27563  nodense  27580  btwncolg1  28458  hlln  28510  btwnlng1  28522  constrllcllem  33715  colineartriv1  36028  weiunso  36427  fnwe2lem3  43014  dfxlim2v  45818  gpgprismgriedgdmss  48016  gpgedgvtx0  48025  gpgvtxedg0  48027  gpgvtxedg1  48028  gpgprismgr4cycllem3  48060  eenglngeehlnmlem2  48700