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Theorem 3mix1 1151
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3mix1 (𝜑 → (𝜑𝜓𝜒))

Proof of Theorem 3mix1
StepHypRef Expression
1 orc 702 . 2 (𝜑 → (𝜑 ∨ (𝜓𝜒)))
2 3orass 966 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
31, 2sylibr 133 1 (𝜑 → (𝜑𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 698  w3o 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699
This theorem depends on definitions:  df-bi 116  df-3or 964
This theorem is referenced by:  3mix2  1152  3mix3  1153  3mix1i  1154  3mix1d  1157  3jaob  1281  nntri3or  6396  elnn0z  9090  nn0le2is012  9156  nn01to3  9435  fztri3or  9849
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