Theorem simprl1 1217

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 1135	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
2	1	ad2antrl 728	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

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:  poxp2  8167  poxp3  8174  pwfseqlem1  10696  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  axcontlem9  29002  axcontlem10  29003  elwspths2spth  29997  wwlksext2clwwlk  30086  locfinref  33802  erdszelem7  35182  cvmlift2lem10  35297  btwnouttr2  36004  btwnconn1lem13  36081  broutsideof2  36104  mpaaeu  43139  dfsalgen2  46297  fundcmpsurinjpreimafv  47333  grtrimap  47851  digexp  48457  line2xlem  48603