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Theorem simp1l1 1267
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1l1 ((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜑)

Proof of Theorem simp1l1
StepHypRef Expression
1 simpl1 1192 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant1 1134 1 ((((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜏𝜂) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1087
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 207  df-an 396  df-3an 1089
This theorem is referenced by:  poxp3  8175  mapxpen  9183  hash7g  14525  lsmcv  21143  sltlpss  27945  archiabl  33205  trisegint  36029  linethru  36154  hlrelat3  39414  cvrval3  39415  cvrval4N  39416  2atlt  39441  atbtwnex  39450  1cvratlt  39476  atcvrlln2  39521  atcvrlln  39522  2llnmat  39526  lplnexllnN  39566  lvolnlelpln  39587  lnjatN  39782  lncvrat  39784  lncmp  39785  cdlemd9  40208  dihord5b  41261  dihmeetALTN  41329  dih1dimatlem0  41330  mapdrvallem2  41647  grumnudlem  44304
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