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 1139	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	ad2antrl 727	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

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:  poxp3  8136  ttrcltr  9711  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  27586  f1otrg  28122  ax5seglem6  28192  axcontlem10  28231  numclwwlk5  29641  locfinref  32821  btwnouttr2  34994  btwnconn1lem13  35071  midofsegid  35076  outsideofeq  35102  ivthALT  35220  mpaaeu  41892  dfsalgen2  45057