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Theorem simp113 1404
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 1263 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant1 1164 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)
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:  axcontlem4  26203  llncvrlpln2  35577  4atlem12b  35631  2lnat  35804  cdlemblem  35813  4atexlemex6  36094  cdleme24  36372  cdleme26ee  36380  cdlemg2idN  36616  dihglblem2N  37314  0ellimcdiv  40620  limclner  40622
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