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Theorem 3exp1 1454
Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3exp1.1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
3exp1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem 3exp1
StepHypRef Expression
1 3exp1.1 . . 3 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜏)
21ex 399 . 2 ((𝜑𝜓𝜒) → (𝜃𝜏))
323exp 1141 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1100
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-an 385  df-3an 1102
This theorem is referenced by:  3an1rs  1461  ltmpi  10011  cshf1  13780  lcmfunsnlem  15573  mulginvcom  17769  symgfvne  18009  voliunlem3  23533  3cyclfrgrrn  27461  numclwwlk1lem2foa  27533  frgrregord013  27583  strlem3a  29439  hstrlem3a  29447  chirredlem1  29577  nn0prpwlem  32638  matunitlindflem1  33718  zerdivemp1x  34057  athgt  35236  paddasslem14  35613  paddidm  35621  tendospcanN  36804  jm2.26  38070  relexpxpmin  38509  0ellimcdiv  40361
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