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 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	ad2antrl 728	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  poxp3  8129  ttrcltr  9669  pwfseqlem5  10616  icodiamlt  15404  issubc3  17811  pgpfac1lem5  20011  clsconn  23317  txlly  23523  txnlly  23524  itg2add  25660  ftc1a  25944  nosupprefixmo  27612  noinfprefixmo  27613  nosupbnd2  27628  noinfbnd2  27643  mulsprop  28033  f1otrg  28798  ax5seglem6  28861  axcontlem10  28900  numclwwlk5  30317  locfinref  33831  btwnouttr2  36010  btwnconn1lem13  36087  midofsegid  36092  outsideofeq  36118  ivthALT  36323  mpaaeu  43139  dfsalgen2  46339  grtrimap  47947