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Theorem simprl1 1219
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Assertion
Ref Expression
simprl1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Proof of Theorem simprl1
StepHypRef Expression
1 simp1 1137 . 2 ((𝜑𝜓𝜒) → 𝜑)
21ad2antrl 727 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  poxp2  8080  poxp3  8087  pwfseqlem1  10601  pwfseqlem5  10606  icodiamlt  15327  issubc3  17742  pgpfac1lem5  19865  clsconn  22797  txlly  23003  txnlly  23004  itg2add  25140  ftc1a  25417  nosupprefixmo  27064  noinfprefixmo  27065  nosupbnd2  27080  noinfbnd2  27095  f1otrg  27855  ax5seglem6  27925  axcontlem9  27963  axcontlem10  27964  elwspths2spth  28954  wwlksext2clwwlk  29043  locfinref  32462  erdszelem7  33831  cvmlift2lem10  33946  btwnouttr2  34636  btwnconn1lem13  34713  broutsideof2  34736  mpaaeu  41506  dfsalgen2  44656  fundcmpsurinjpreimafv  45674  digexp  46767  line2xlem  46913
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