Theorem 3mix2 1332

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

Ref	Expression
3mix2	⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

Proof of Theorem 3mix2

Step	Hyp	Ref	Expression
1		3mix1 1331	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓))
2		3orrot 1091	. 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))
3	1, 2	sylibr 234	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

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:  3mix2i  1335  3mix2d  1338  3jaobOLD  1429  tppreqb  4754  tpres  7135  onzsl  7776  sornom  10168  nnz  12489  nn0le2is012  12537  hash1to3  14399  cshwshashlem1  17007  zabsle1  27234  ostth  27577  nolesgn2o  27610  nogesgn1o  27612  sltsolem1  27614  nosep1o  27620  nosep2o  27621  nodenselem8  27630  fnwe2lem3  43093  dfxlim2v  45893