Theorem 3mix2d 1422

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 1416	. 2 ⊢ (𝜓 → (𝜒 ∨ 𝜓 ∨ 𝜃))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜒 ∨ 𝜓 ∨ 𝜃))

Syntax hints:   → wi 4   ∨ w3o 1071

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 197  df-or 384  df-3or 1073

This theorem is referenced by:  sosn  5345  funtpgOLD  6104  f1dom3fv3dif  6688  f1dom3el3dif  6689  elfiun  8501  fpwwe2lem13  9656  lcmfunsnlem2lem2  15554  dyaddisjlem  23563  tgcolg  25648  btwncolg2  25650  hlln  25701  btwnlng2  25714  frgrregorufr0  27478  sltsolem1  32132  colineartriv2  32481