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Theorem 3mix2 1168
Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)
Assertion
Ref Expression
3mix2 (𝜑 → (𝜓𝜑𝜒))

Proof of Theorem 3mix2
StepHypRef Expression
1 3mix1 1167 . 2 (𝜑 → (𝜑𝜒𝜓))
2 3orrot 985 . 2 ((𝜓𝜑𝜒) ↔ (𝜑𝜒𝜓))
31, 2sylibr 134 1 (𝜑 → (𝜓𝜑𝜒))
Colors of variables: wff set class
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
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