Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp211 Structured version   Visualization version   GIF version

Theorem simp211 1307
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp211 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜑)

Proof of Theorem simp211
StepHypRef Expression
1 simp11 1199 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant2 1130 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1083 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 1085 This theorem is referenced by:  cdleme27a  37502  cdlemk5u  37996  cdlemk6u  37997  cdlemk7u  38005  cdlemk11u  38006  cdlemk12u  38007  cdlemk7u-2N  38023  cdlemk11u-2N  38024  cdlemk12u-2N  38025  cdlemk20-2N  38027  cdlemk22  38028  cdlemk33N  38044  cdlemk53b  38091  cdlemk53  38092  cdlemk55a  38094  cdlemkyyN  38097  cdlemk43N  38098
 Copyright terms: Public domain W3C validator