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Theorem simprr2 1275
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Assertion
Ref Expression
simprr2 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Proof of Theorem simprr2
StepHypRef Expression
1 simp2 1132 . 2 ((𝜑𝜓𝜒) → 𝜓)
21ad2antll 767 1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 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  psgnunilem2  18136  haust1  21379  cnhaus  21381  isreg2  21404  llynlly  21503  restnlly  21508  llyrest  21511  llyidm  21514  nllyidm  21515  cldllycmp  21521  txlly  21662  txnlly  21663  pthaus  21664  txhaus  21673  txkgen  21678  xkohaus  21679  xkococnlem  21685  cmetcaulem  23307  itg2add  23746  ulmdvlem3  24376  ax5seglem6  26035  n4cyclfrgr  27467  connpconn  31546  cvmlift3lem2  31631  cvmlift3lem8  31637  noprefixmo  32176  scutbdaybnd  32249  broutsideof3  32561  unblimceq0  32826  paddasslem10  35637  lhpexle2lem  35817  lhpexle3lem  35819  stoweidlem35  40774  stoweidlem56  40795  stoweidlem59  40798
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