Theorem 3mix1d 1355

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 1349	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜒 ∨ 𝜃))
3	1, 2	syl 18	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜃))

This proof depends on syntax axioms:   → wi 4   ∨ w3o 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-3or 1104

This theorem is used by:  f1dom3fv3dif  7271  f1dom3el3dif  7272  xpord3inddlem  8156  elfiun  9397  prinfzo0  13744  fvf1tp  13840  lcmfunsnlem2lem2  16719  estrreslem2  18216  ostth  27854  noextendlt  27884  ltssolem1  27890  nodense  27907  btwncolg1  28875  hlln  28930  btwnlng1  28943  elplnglnid  29116  constrllcllem  34206  colineartriv1  36596  weiunso  37034  fnwe2lem3  43837  dfxlim2v  46619  gpgprismgriedgdmss  48875  gpgedgvtx0  48884  gpgvtxedg0  48886  gpgvtxedg1  48887  gpgprismgr4cycllem3  48920  eenglngeehlnmlem2  49575