MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simprl3 Structured version   Visualization version   GIF version

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 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simprl3
StepHypRef Expression
1 simp3 1131 . 2 ((𝜑𝜓𝜒) → 𝜒)
21ad2antrl 699 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)
Colors of variables: wff setvar class
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
  Copyright terms: Public domain W3C validator