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Theorem simp1lr 1145
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp1lr ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃𝜏) → 𝜓)

Proof of Theorem simp1lr
StepHypRef Expression
1 simplr 807 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜓)
213ad2ant1 1102 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃𝜏) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1054
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 1056
This theorem is referenced by:  lspsolvlem  19190  dmatcrng  20356  scmatcrng  20375  1marepvsma1  20437  mdetunilem7  20472  mat2pmatghm  20583  pmatcollpwscmatlem2  20643  mp2pm2mplem4  20662  ax5seg  25863  measinblem  30411  btwnconn1lem13  32331  athgt  35060  llnle  35122  lplnle  35144  lhpexle1  35612  lhpat3  35650  tendoicl  36401  cdlemk55b  36565  pellex  37716  ssfiunibd  39837  mullimc  40166  mullimcf  40173  icccncfext  40418  etransclem32  40801
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