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Theorem simp113 1301
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 1202 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant1 1130 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084
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 206  df-an 395  df-3an 1086
This theorem is referenced by:  axcontlem4  28901  llncvrlpln2  39256  4atlem12b  39310  2lnat  39483  cdlemblem  39492  4atexlemex6  39773  cdleme24  40051  cdleme26ee  40059  cdlemg2idN  40295  dihglblem2N  40993  0ellimcdiv  45270  limclner  45272
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