Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp213 Structured version   Visualization version   GIF version

Theorem simp213 1310
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp213 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)

Proof of Theorem simp213
StepHypRef Expression
1 simp13 1202 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant2 1131 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1084 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 1086 This theorem is referenced by:  cdleme27a  37814  cdlemk5u  38308  cdlemk6u  38309  cdlemk7u  38317  cdlemk11u  38318  cdlemk12u  38319  cdlemk7u-2N  38335  cdlemk11u-2N  38336  cdlemk12u-2N  38337  cdlemk20-2N  38339  cdlemk22  38340  cdlemk22-3  38348  cdlemk33N  38356  cdlemk53b  38403  cdlemk53  38404  cdlemk55a  38406  cdlemkyyN  38409  cdlemk43N  38410
 Copyright terms: Public domain W3C validator