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Theorem 3exp1 1275
 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 449 . 2 ((𝜑𝜓𝜒) → (𝜃𝜏))
323exp 1256 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  ltmpi  9605  cshf1  13407  lcmfunsnlem  15192  mulginvcom  17388  symgfvne  17631  voliunlem3  23127  frgraregord013  26645  strlem3a  28495  hstrlem3a  28503  chirredlem1  28633  nn0prpwlem  31487  matunitlindflem1  32575  zerdivemp1x  32916  athgt  33760  paddasslem14  34137  paddidm  34145  tendospcanN  35330  jm2.26  36587  relexpxpmin  37028  0ellimcdiv  38716  3cyclfrgrrn  41456  av-frgraregord013  41549
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