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Theorem simpl1 907
Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)
Assertion
Ref Expression
simpl1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)

Proof of Theorem simpl1
StepHypRef Expression
1 simp1 904 . 2 ((𝜑𝜓𝜒) → 𝜑)
21adantr 261 1 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  simpll1  943  simprl1  949  simp1l1  997  simp2l1  1003  simp3l1  1009  3anandirs  1238  rspc3ev  2663  brcogw  4491  cocan1  5414  oawordi  6036  nnmord  6077  nnmword  6078  dif1en  6324  ac6sfi  6338  enq0tr  6513  distrlem4prl  6663  distrlem4pru  6664  ltaprg  6698  aptiprlemu  6719  lelttr  7086  readdcan  7133  addcan  7171  addcan2  7172  ltadd2  7395  ltmul1a  7558  ltmul1  7559  lemul1a  7800  xrlelttr  8689  icoshftf1o  8826  lincmb01cmp  8838  iccf1o  8839  fztri3or  8870  fzofzim  9011  ltexp2a  9184  exple1  9188  expnlbnd2  9252  addcn2  9708  mulcn2  9710
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