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Theorem simprr3 1224
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Assertion
Ref Expression
simprr3 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simprr3
StepHypRef Expression
1 simp3 1139 . 2 ((𝜑𝜓𝜒) → 𝜒)
21ad2antll 728 1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
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:  el2xptp0  8022  poxp2  8129  ttrcltr  9711  icodiamlt  15382  psgnunilem2  19363  srgbinom  20054  psgndiflemA  21154  haust1  22856  cnhaus  22858  isreg2  22881  llynlly  22981  restnlly  22986  llyrest  22989  llyidm  22992  nllyidm  22993  cldllycmp  22999  txlly  23140  txnlly  23141  pthaus  23142  txhaus  23151  txkgen  23156  xkohaus  23157  xkococnlem  23163  cmetcaulem  24805  itg2add  25277  ulmdvlem3  25914  nosupprefixmo  27203  noinfprefixmo  27204  nosupno  27206  noinfno  27221  etasslt  27314  scutbdaybnd  27316  scutbdaybnd2  27317  addsproplem6  27458  negsproplem6  27507  mulsproplem13  27584  mulsproplem14  27585  mulsprop  27586  ax5seglem6  28192  fusgrfis  28587  wwlksnextfun  29152  umgr2wlkon  29204  connpconn  34226  cvmlift3lem2  34311  cvmlift3lem8  34317  ifscgr  35016  broutsideof3  35098  unblimceq0  35383  paddasslem10  38700  lhpexle2lem  38880  lhpexle3lem  38882  mpaaeu  41892  stoweidlem35  44751  stoweidlem56  44772  stoweidlem59  44775
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