Theorem 3mix2 1168

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 1167	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓))
2		3orrot 985	. 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))
3	1, 2	sylibr 134	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ w3o 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117  df-3or 980

This theorem is referenced by:  3mix2i  1171  3mix2d  1174  3jaob  1312  funtpg  5279  elnn0z  9280  nn0le2is012  9349  nn01to3  9631  zabsle1  14753  triap  15131