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Theorem simp111 1402
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 1261 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant1 1164 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  tsmsxp  22286  ps-2b  35503  llncvrlpln2  35578  4atlem11b  35629  4atlem12b  35632  lplncvrlvol2  35636  lneq2at  35799  2lnat  35805  cdlemblem  35814  4atexlemex6  36095  cdleme24  36373  cdleme26ee  36381  cdlemg2idN  36617  cdlemg31c  36720  cdlemk26-3  36927  0ellimcdiv  40625
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