Theorem 3mix3 1126

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

Assertion

Ref	Expression
3mix3	⊢ (φ → (ψ ∨ χ ∨ φ))

Proof of Theorem 3mix3

Step	Hyp	Ref	Expression
1		3mix1 1124	. 2 ⊢ (φ → (φ ∨ ψ ∨ χ))
2		3orrot 940	. 2 ⊢ ((φ ∨ ψ ∨ χ) ↔ (ψ ∨ χ ∨ φ))
3	1, 2	sylib 188	1 ⊢ (φ → (ψ ∨ χ ∨ φ))

Syntax hints:   → wi 4   ∨ w3o 933

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 177  df-or 359  df-3or 935

This theorem is referenced by:  3mix3i  1129  3jaob  1244  tpid3g  3832  ltfintri  4467