MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp33r Structured version   Visualization version   GIF version

Theorem simp33r 1187
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp33r ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Proof of Theorem simp33r
StepHypRef Expression
1 simp3r 1088 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜓)
213ad2ant3 1082 1 ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  totprob  30282  cdleme19b  35093  cdleme19e  35096  cdleme20h  35105  cdleme20l2  35110  cdleme20m  35112  cdleme21d  35119  cdleme21e  35120  cdleme22eALTN  35134  cdleme22f2  35136  cdleme22g  35137  cdleme26e  35148  cdleme37m  35251  cdlemeg46gfre  35321  cdlemg28a  35482  cdlemg28b  35492  cdlemk5a  35624  cdlemk6  35626
  Copyright terms: Public domain W3C validator