Theorem simprl1 1219

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

Assertion

Ref	Expression
simprl1	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Proof of Theorem simprl1

Step	Hyp	Ref	Expression
1		simp1 1137	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
2	1	ad2antrl 728	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  poxp2  8168  poxp3  8175  pwfseqlem1  10698  pwfseqlem5  10703  icodiamlt  15474  issubc3  17894  pgpfac1lem5  20099  clsconn  23438  txlly  23644  txnlly  23645  itg2add  25794  ftc1a  26078  nosupprefixmo  27745  noinfprefixmo  27746  nosupbnd2  27761  noinfbnd2  27776  mulsprop  28156  f1otrg  28879  ax5seglem6  28949  axcontlem9  28987  axcontlem10  28988  elwspths2spth  29987  wwlksext2clwwlk  30076  locfinref  33840  erdszelem7  35202  cvmlift2lem10  35317  btwnouttr2  36023  btwnconn1lem13  36100  broutsideof2  36123  mpaaeu  43162  dfsalgen2  46356  fundcmpsurinjpreimafv  47395  grtrimap  47915  digexp  48528  line2xlem  48674