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

Theorem simp211 1311
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 1203 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant2 1134 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1087
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 206  df-an 397  df-3an 1089
This theorem is referenced by:  cdleme27a  39043  cdlemk5u  39537  cdlemk6u  39538  cdlemk7u  39546  cdlemk11u  39547  cdlemk12u  39548  cdlemk7u-2N  39564  cdlemk11u-2N  39565  cdlemk12u-2N  39566  cdlemk20-2N  39568  cdlemk22  39569  cdlemk33N  39585  cdlemk53b  39632  cdlemk53  39633  cdlemk55a  39635  cdlemkyyN  39638  cdlemk43N  39639
  Copyright terms: Public domain W3C validator