Theorem simprl3 1221

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

Assertion

Ref	Expression
simprl3	⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simprl3

Step	Hyp	Ref	Expression
1		simp3 1139	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	ad2antrl 728	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

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:  poxp3  8175  ttrcltr  9756  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  axcontlem10  28988  numclwwlk5  30407  locfinref  33840  btwnouttr2  36023  btwnconn1lem13  36100  midofsegid  36105  outsideofeq  36131  ivthALT  36336  mpaaeu  43162  dfsalgen2  46356  grtrimap  47915