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Theorem simprl3 1270
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Assertion
Ref Expression
simprl3 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simprl3
StepHypRef Expression
1 simp3 1132 . 2 ((𝜑𝜓𝜒) → 𝜒)
21ad2antrl 707 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382   ∧ w3a 1071 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 383  df-3an 1073 This theorem is referenced by:  pwfseqlem5  9687  icodiamlt  14382  issubc3  16716  pgpfac1lem5  18686  clsconn  21454  txlly  21660  txnlly  21661  itg2add  23746  ftc1a  24020  f1otrg  25972  ax5seglem6  26035  axcontlem10  26074  numclwwlk5  27587  locfinref  30248  noprefixmo  32185  nosupbnd2  32199  btwnouttr2  32466  btwnconn1lem13  32543  midofsegid  32548  outsideofeq  32574  ivthALT  32667  mpaaeu  38246  dfsalgen2  41076
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