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Theorem simprl2 1269
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Assertion
Ref Expression
simprl2 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)

Proof of Theorem simprl2
StepHypRef Expression
1 simp2 1132 . 2 ((𝜑𝜓𝜒) → 𝜓)
21ad2antrl 766 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1072 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 1074 This theorem is referenced by:  icodiamlt  14394  issubc3  16731  clsconn  21456  txlly  21662  txnlly  21663  itg2add  23746  ftc1a  24020  f1otrg  25972  ax5seglem6  26035  axcontlem9  26073  axcontlem10  26074  clwwlkf  27198  locfinref  30239  erdszelem7  31508  noprefixmo  32176  nosupbnd2  32190  btwnconn1lem13  32534  dfsalgen2  41081
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