MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simpr3r Structured version   Visualization version   GIF version

Theorem simpr3r 1230
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpr3r ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Proof of Theorem simpr3r
StepHypRef Expression
1 simprr 771 . 2 ((𝜏 ∧ (𝜑𝜓)) → 𝜓)
213ad2antr3 1185 1 ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1082
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 209  df-an 399  df-3an 1084
This theorem is referenced by:  ax5seg  26716  segconeq  33464  ifscgr  33498  btwnconn1lem9  33549  btwnconn1lem11  33551  btwnconn1lem12  33552  lplnexllnN  36692  cdleme3b  37357  cdleme3c  37358  cdleme3e  37360  cdleme27a  37495
  Copyright terms: Public domain W3C validator