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Theorem 3mix1 1118
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 674 . 2 (𝜑 → (𝜑 ∨ (𝜓𝜒)))
2 3orass 933 . 2 ((𝜑𝜓𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
31, 2sylibr 133 1 (𝜑 → (𝜑𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 670  w3o 929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671
This theorem depends on definitions:  df-bi 116  df-3or 931
This theorem is referenced by:  3mix2  1119  3mix3  1120  3mix1i  1121  3mix1d  1124  3jaob  1248  nntri3or  6319  elnn0z  8919  nn0le2is012  8985  nn01to3  9259  fztri3or  9660
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