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Theorem simp113 1300
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 1201 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜒)
213ad2ant1 1129 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by:  axcontlem4  26752  llncvrlpln2  36692  4atlem12b  36746  2lnat  36919  cdlemblem  36928  4atexlemex6  37209  cdleme24  37487  cdleme26ee  37495  cdlemg2idN  37731  dihglblem2N  38429  0ellimcdiv  41930  limclner  41932
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