Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp212 Structured version   Visualization version   GIF version

Theorem simp212 1309
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp212 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)

Proof of Theorem simp212
StepHypRef Expression
1 simp12 1201 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant2 1131 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜓)
 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  37608  cdlemk5u  38102  cdlemk6u  38103  cdlemk7u  38111  cdlemk11u  38112  cdlemk12u  38113  cdlemk7u-2N  38129  cdlemk11u-2N  38130  cdlemk12u-2N  38131  cdlemk20-2N  38133  cdlemk22  38134  cdlemk22-3  38142  cdlemk33N  38150  cdlemk53b  38197  cdlemk53  38198  cdlemk55a  38200  cdlemkyyN  38203  cdlemk43N  38204
 Copyright terms: Public domain W3C validator