Theorem 3mix2 1350

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 1349	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓))
2		3orrot 1108	. 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))
3	1, 2	sylibr 237	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

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:  3mix2i  1353  3mix2d  1356  tppreqb  4775  tpres  7206  onzsl  7848  sornom  10276  nnz  12627  nn0le2is012  12676  hash1to3  14547  cshwshashlem1  17177  zabsle1  27511  ostth  27854  nolesgn2o  27886  nogesgn1o  27888  ltssolem1  27890  nosep1o  27896  nosep2o  27897  nodenselem8  27906  fnwe2lem3  43837  dfxlim2v  46619