MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp111 Structured version   Visualization version   GIF version

Theorem simp111 1296
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp111 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)

Proof of Theorem simp111
StepHypRef Expression
1 simp11 1197 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant1 1127 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)
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:  tsmsxp  22697  ps-2b  36504  llncvrlpln2  36579  4atlem11b  36630  4atlem12b  36633  lplncvrlvol2  36637  lneq2at  36800  2lnat  36806  cdlemblem  36815  4atexlemex6  37096  cdleme24  37374  cdleme26ee  37382  cdlemg2idN  37618  cdlemg31c  37721  cdlemk26-3  37928  0ellimcdiv  41814
  Copyright terms: Public domain W3C validator