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Theorem 3mix2 1085
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 1084 . 2 (𝜑 → (𝜑𝜒𝜓))
2 3orrot 902 . 2 ((𝜓𝜑𝜒) ↔ (𝜑𝜒𝜓))
31, 2sylibr 141 1 (𝜑 → (𝜓𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  w3o 895
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114  df-3or 897
This theorem is referenced by:  3mix2i  1088  3mix2d  1091  3jaob  1208  funtpg  4978  elnn0z  8315  nn01to3  8649
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