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Theorem simp1l 1005
Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
Assertion
Ref Expression
simp1l (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜑)

Proof of Theorem simp1l
StepHypRef Expression
1 simpl 108 . 2 ((𝜑𝜓) → 𝜑)
213ad2ant1 1002 1 (((𝜑𝜓) ∧ 𝜒𝜃) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  simpl1l  1032  simpr1l  1038  simp11l  1092  simp21l  1098  simp31l  1104  en2lp  4469  tfisi  4501  funprg  5173  nnsucsssuc  6388  ecopovtrn  6526  ecopovtrng  6529  addassnqg  7202  distrnqg  7207  ltsonq  7218  ltanqg  7220  ltmnqg  7221  distrnq0  7279  addassnq0  7282  mulasssrg  7578  distrsrg  7579  lttrsr  7582  ltsosr  7584  ltasrg  7590  mulextsr1lem  7600  mulextsr1  7601  axmulass  7693  axdistr  7694  dmdcanap  8494  lt2msq1  8655  ltdiv2  8657  lediv2  8661  xaddass  9664  xaddass2  9665  xlt2add  9675  modqdi  10177  expaddzaplem  10348  expaddzap  10349  expmulzap  10351  resqrtcl  10813  bdtrilem  11022  bdtri  11023  xrbdtri  11057  prmexpb  11840  cnptoprest  12422  ssblps  12608  ssbl  12609
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