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Theorem 3exp1 1444
 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 397 . 2 ((𝜑𝜓𝜒) → (𝜃𝜏))
323exp 1111 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382   ∧ w3a 1070 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 197  df-an 383  df-3an 1072 This theorem is referenced by:  3an1rs  1451  ltmpi  9927  cshf1  13764  lcmfunsnlem  15561  mulginvcom  17772  symgfvne  18014  voliunlem3  23539  3cyclfrgrrn  27465  numclwlk1lem2foa  27538  frgrregord013  27588  strlem3a  29445  hstrlem3a  29453  chirredlem1  29583  nn0prpwlem  32648  matunitlindflem1  33731  zerdivemp1x  34071  athgt  35257  paddasslem14  35634  paddidm  35642  tendospcanN  36826  jm2.26  38088  relexpxpmin  38528  0ellimcdiv  40393
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