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  8090  ttrcltr  9631  pwfseqlem5  10576  icodiamlt  15363  issubc3  17774  pgpfac1lem5  19978  clsconn  23333  txlly  23539  txnlly  23540  itg2add  25676  ftc1a  25960  nosupprefixmo  27628  noinfprefixmo  27629  nosupbnd2  27644  noinfbnd2  27659  mulsprop  28056  f1otrg  28834  ax5seglem6  28897  axcontlem10  28936  numclwwlk5  30350  locfinref  33810  btwnouttr2  35998  btwnconn1lem13  36075  midofsegid  36080  outsideofeq  36106  ivthALT  36311  mpaaeu  43126  dfsalgen2  46326  grtrimap  47936