Theorem 3mix1 817

Description: Introduction in triple disjunction.

Assertion

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

Proof of Theorem 3mix1

Step	Hyp	Ref	Expression
1		orc 269	. 2 ⊢ (φ → (φ ⋁ (ψ ⋁ χ)))
2		3orass 780	. 2 ⊢ ((φ ⋁ ψ ⋁ χ) ↔ (φ ⋁ (ψ ⋁ χ)))
3	1, 2	sylibr 200	1 ⊢ (φ → (φ ⋁ ψ ⋁ χ))

Syntax hints:   → wi 3   ⋁ wo 222   ⋁ w3o 776

This theorem is referenced by:  3mix2 818  3mix3 819  tz7.44-1 3934

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-3or 778

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