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Theorem 3imp1 1128
Description: Importation to left triple conjunction. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3imp1.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
3imp1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem 3imp1
StepHypRef Expression
1 3imp1.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
213imp 1109 . 2 ((𝜑𝜓𝜒) → (𝜃𝜏))
32imp 119 1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
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
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  reupick2  3251  ledivge1le  8750  leexp1a  9475
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