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Theorem 3impib 1201
Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)
Hypothesis
Ref Expression
3impib.1 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
3impib ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem 3impib
StepHypRef Expression
1 3impib.1 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
21expd 258 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
323imp 1193 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  mob  2920  eqreu  2930  iotam  5209  funimaexglem  5300  ssimaexg  5579  rbropap  6244  dfsmo2  6288  3ecoptocl  6624  distrnq0  7458  addassnq0  7461  uzind  9364  fzind  9368  fnn0ind  9369  xltnegi  9835  facwordi  10720  shftvalg  10845  shftval4g  10846  mulgcd  12017  coprmdvds1  12091  pcfac  12348  mgmcl  12778  mhmlin  12858  mhmmulg  13024  issubg2m  13049  nsgbi  13064  srgmulgass  13172  dvdsrtr  13270  issubrg2  13362  inopn  13506  basis1  13550  cnmpt2t  13796  cnmpt22  13797  cnmptcom  13801  xmeteq0  13862  sincosq1sgn  14250  sincosq2sgn  14251  sincosq3sgn  14252  sincosq4sgn  14253  speano5  14699
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