Theorem simprl1 1219

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 1137	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
2	1	ad2antrl 727	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 397   ∧ w3a 1088

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 398  df-3an 1090

This theorem is referenced by:  poxp2  8129  poxp3  8136  pwfseqlem1  10653  pwfseqlem5  10658  icodiamlt  15382  issubc3  17799  pgpfac1lem5  19949  clsconn  22934  txlly  23140  txnlly  23141  itg2add  25277  ftc1a  25554  nosupprefixmo  27203  noinfprefixmo  27204  nosupbnd2  27219  noinfbnd2  27234  mulsprop  27589  f1otrg  28153  ax5seglem6  28223  axcontlem9  28261  axcontlem10  28262  elwspths2spth  29252  wwlksext2clwwlk  29341  locfinref  32852  erdszelem7  34219  cvmlift2lem10  34334  btwnouttr2  35025  btwnconn1lem13  35102  broutsideof2  35125  mpaaeu  41940  dfsalgen2  45105  fundcmpsurinjpreimafv  46124  digexp  47341  line2xlem  47487