MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp3r2 Structured version   Visualization version   GIF version

Theorem simp3r2 1284
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r2 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Proof of Theorem simp3r2
StepHypRef Expression
1 simpr2 1197 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1137 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1089
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 210  df-an 400  df-3an 1091
This theorem is referenced by:  nllyrest  22407  cdlemblem  37571  cdleme21  38115  cdleme22b  38119  cdleme40m  38245  cdlemg34  38490  cdlemk5u  38639  cdlemk6u  38640  cdlemk21N  38651  cdlemk20  38652  cdlemk26b-3  38683  cdlemk26-3  38684  cdlemk28-3  38686  cdlemky  38704  cdlemk11t  38724  cdlemkyyN  38740  stoweidlem56  43301
  Copyright terms: Public domain W3C validator