Theorem simprr1 1222

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

Assertion

Ref	Expression
simprr1	⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

Proof of Theorem simprr1

Step	Hyp	Ref	Expression
1		simp1 1137	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
2	1	ad2antll 728	1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑)

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:  poxp2  8129  sqrmo  15198  icodiamlt  15382  psgnunilem2  19363  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  hauspwpwf1  23491  itg2add  25277  ulmdvlem3  25914  nosupno  27206  noinfno  27221  etasslt  27314  scutbdaybnd  27316  scutbdaybnd2  27317  addsproplem6  27458  negsproplem6  27507  mulsproplem13  27584  mulsproplem14  27585  mulsprop  27586  ax5seglem6  28192  fusgrfis  28587  umgr2wlkon  29204  numclwwlk5  29641  connpconn  34226  cvmliftmolem2  34273  cvmlift2lem10  34303  cvmlift3lem2  34311  cvmlift3lem8  34317  broutsideof3  35098  unblimceq0  35383  paddasslem10  38700  lhpexle2lem  38880  lhpexle3lem  38882  cdlemj3  39694  cdlemkid4  39805  mpaaeu  41892  stoweidlem35  44751  stoweidlem56  44772  stoweidlem59  44775