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Theorem simp113 1388
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp113 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)

Proof of Theorem simp113
StepHypRef Expression
1 simp13 1247 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant1 1127 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1071
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 197  df-an 383  df-3an 1073
This theorem is referenced by:  axcontlem4  26068  llncvrlpln2  35365  4atlem12b  35419  2lnat  35592  cdlemblem  35601  4atexlemex6  35882  cdleme24  36161  cdleme26ee  36169  cdlemg2idN  36405  dihglblem2N  37104  0ellimcdiv  40399  limclner  40401
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