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Theorem pm3.2an3 1094
Description: pm3.2 130 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.)
Assertion
Ref Expression
pm3.2an3 (𝜑 → (𝜓 → (𝜒 → (𝜑𝜓𝜒))))

Proof of Theorem pm3.2an3
StepHypRef Expression
1 pm3.2 130 . . 3 ((𝜑𝜓) → (𝜒 → ((𝜑𝜓) ∧ 𝜒)))
21ex 112 . 2 (𝜑 → (𝜓 → (𝜒 → ((𝜑𝜓) ∧ 𝜒))))
3 df-3an 898 . . 3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
43bicomi 127 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜑𝜓𝜒))
52, 4syl8ib 159 1 (𝜑 → (𝜓 → (𝜒 → (𝜑𝜓𝜒))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  3exp  1114
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