Theorem simprl1 1218

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 1136	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
2	1	ad2antrl 726	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1089

This theorem is referenced by:  poxp2  8128  poxp3  8135  pwfseqlem1  10652  pwfseqlem5  10657  icodiamlt  15381  issubc3  17798  pgpfac1lem5  19948  clsconn  22933  txlly  23139  txnlly  23140  itg2add  25276  ftc1a  25553  nosupprefixmo  27200  noinfprefixmo  27201  nosupbnd2  27216  noinfbnd2  27231  mulsprop  27583  f1otrg  28119  ax5seglem6  28189  axcontlem9  28227  axcontlem10  28228  elwspths2spth  29218  wwlksext2clwwlk  29307  locfinref  32816  erdszelem7  34183  cvmlift2lem10  34298  btwnouttr2  34989  btwnconn1lem13  35066  broutsideof2  35089  mpaaeu  41882  dfsalgen2  45047  fundcmpsurinjpreimafv  46066  digexp  47283  line2xlem  47429