Theorem simprl3 1269

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 1131	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	ad2antrl 699	1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 382   ∧ w3a 1070

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 197  df-an 383  df-3an 1072

This theorem is referenced by:  pwfseqlem5  9686  icodiamlt  14381  issubc3  16715  pgpfac1lem5  18685  clsconn  21453  txlly  21659  txnlly  21660  itg2add  23745  ftc1a  24019  f1otrg  25971  ax5seglem6  26034  axcontlem10  26073  numclwwlk5  27581  locfinref  30242  noprefixmo  32179  nosupbnd2  32193  btwnouttr2  32460  btwnconn1lem13  32537  midofsegid  32542  outsideofeq  32568  ivthALT  32661  mpaaeu  38239  dfsalgen2  41070