Theorem simprr3 1277

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)

Assertion

Ref	Expression
simprr3	⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simprr3

Step	Hyp	Ref	Expression
1		simp3 1133	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	ad2antll 767	1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

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:  el2xptp0  7381  icodiamlt  14394  psgnunilem2  18136  srgbinom  18766  psgndiflemA  20170  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  fusgrfis  26443  wwlksnextfun  27038  umgr2wlkon  27092  connpconn  31546  cvmlift3lem2  31631  cvmlift3lem8  31637  noprefixmo  32176  nosupno  32177  scutbdaybnd  32249  ifscgr  32479  broutsideof3  32561  unblimceq0  32826  paddasslem10  35637  lhpexle2lem  35817  lhpexle3lem  35819  mpaaeu  38241  stoweidlem35  40774  stoweidlem56  40795  stoweidlem59  40798