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Theorem 3impd 1157
Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3imp1.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
3impd (𝜑 → ((𝜓𝜒𝜃) → 𝜏))

Proof of Theorem 3impd
StepHypRef Expression
1 3imp1.1 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21com4l 83 . . 3 (𝜓 → (𝜒 → (𝜃 → (𝜑𝜏))))
323imp 1137 . 2 ((𝜓𝜒𝜃) → (𝜑𝜏))
43com12 30 1 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  3imp2  1158  3impexp  1371  oprabid  5663  iccid  9312
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