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Theorem simp113 1296
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 1197 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant1 1125 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1079
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 1081
This theorem is referenced by:  axcontlem4  26680  llncvrlpln2  36573  4atlem12b  36627  2lnat  36800  cdlemblem  36809  4atexlemex6  37090  cdleme24  37368  cdleme26ee  37376  cdlemg2idN  37612  dihglblem2N  38310  0ellimcdiv  41806  limclner  41808
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