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Theorem pm3.2an3 1145
Description: pm3.2 138 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 pm3.2 138 . . 3 ((𝜑𝜓) → (𝜒 → ((𝜑𝜓) ∧ 𝜒)))
21ex 114 . 2 (𝜑 → (𝜓 → (𝜒 → ((𝜑𝜓) ∧ 𝜒))))
3 df-3an 949 . . 3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
43bicomi 131 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜑𝜓𝜒))
52, 4syl8ib 165 1 (𝜑 → (𝜓 → (𝜒 → (𝜑𝜓𝜒))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  3exp  1165
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