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Theorem 3imp2 1443
Description: Importation to right triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3imp1.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
3imp2 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)

Proof of Theorem 3imp2
StepHypRef Expression
1 3imp1.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
213impd 1442 . 2 (𝜑 → ((𝜓𝜒𝜃) → 𝜏))
32imp 444 1 ((𝜑 ∧ (𝜓𝜒𝜃)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 385  df-3an 1074
This theorem is referenced by:  wereu  5262  ovg  6964  fisup2g  8539  fiinf2g  8571  cfcoflem  9286  ttukeylem5  9527  dedekindle  10393  grplcan  17678  mulgnnass  17777  mulgnnassOLD  17778  dmdprdsplit2  18645  mulgass2  18801  lmodvsdi  19088  lmodvsdir  19089  lmodvsass  19090  lss1d  19165  islmhm2  19240  lspsolvlem  19344  lbsextlem2  19361  cygznlem2a  20118  isphld  20201  t0dist  21331  hausnei  21334  nrmsep3  21361  fclsopni  22020  fcfneii  22042  ax5seglem5  26012  axcont  26055  grporcan  27681  grpolcan  27693  slmdvsdi  30077  slmdvsdir  30078  slmdvsass  30079  mclsppslem  31787  broutsideof2  32535  poimirlem31  33753  broucube  33756  frinfm  33843  crngm23  34114  pridl  34149  pridlc  34183  dmnnzd  34187  dmncan1  34188  paddasslem5  35613  sfprmdvdsmersenne  42030
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