Theorem 3mix1 1124

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

Assertion

Ref	Expression
3mix1	⊢ (φ → (φ ∨ ψ ∨ χ))

Proof of Theorem 3mix1

Step	Hyp	Ref	Expression
1		orc 374	. 2 ⊢ (φ → (φ ∨ (ψ ∨ χ)))
2		3orass 937	. 2 ⊢ ((φ ∨ ψ ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))
3	1, 2	sylibr 203	1 ⊢ (φ → (φ ∨ ψ ∨ χ))

Syntax hints:   → wi 4   ∨ wo 357   ∨ 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:  3mix2  1125  3mix3  1126  3mix1i  1127  3jaob  1244  ltfintri  4467  nncdiv3  6278