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Theorem 3mix2 1152
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 1151 . 2 (𝜑 → (𝜑𝜒𝜓))
2 3orrot 969 . 2 ((𝜓𝜑𝜒) ↔ (𝜑𝜒𝜓))
31, 2sylibr 133 1 (𝜑 → (𝜓𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  3mix2i  1155  3mix2d  1158  3jaob  1281  funtpg  5178  elnn0z  9087  nn0le2is012  9153  nn01to3  9432  triap  13382
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