Theorem simprl3 1219

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 1137	. 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  8174  ttrcltr  9754  pwfseqlem5  10701  icodiamlt  15471  issubc3  17900  pgpfac1lem5  20114  clsconn  23454  txlly  23660  txnlly  23661  itg2add  25809  ftc1a  26093  nosupprefixmo  27760  noinfprefixmo  27761  nosupbnd2  27776  noinfbnd2  27791  mulsprop  28171  f1otrg  28894  ax5seglem6  28964  axcontlem10  29003  numclwwlk5  30417  locfinref  33802  btwnouttr2  36004  btwnconn1lem13  36081  midofsegid  36086  outsideofeq  36112  ivthALT  36318  mpaaeu  43139  dfsalgen2  46297  grtrimap  47851