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

Theorem simp213 1307
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 1199 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant2 1128 1 ((𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1081
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 208  df-an 397  df-3an 1083
This theorem is referenced by:  cdleme27a  37370  cdlemk5u  37864  cdlemk6u  37865  cdlemk7u  37873  cdlemk11u  37874  cdlemk12u  37875  cdlemk7u-2N  37891  cdlemk11u-2N  37892  cdlemk12u-2N  37893  cdlemk20-2N  37895  cdlemk22  37896  cdlemk22-3  37904  cdlemk33N  37912  cdlemk53b  37959  cdlemk53  37960  cdlemk55a  37962  cdlemkyyN  37965  cdlemk43N  37966
  Copyright terms: Public domain W3C validator