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Theorem simp112 1304
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp112 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜓)

Proof of Theorem simp112
StepHypRef Expression
1 simp12 1205 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant1 1134 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1088
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 210  df-an 400  df-3an 1090
This theorem is referenced by:  axcontlem4  26905  ps-2b  37108  llncvrlpln2  37183  4atlem11b  37234  4atlem12b  37237  2lnat  37410  cdlemblem  37419  4atexlemex6  37700  cdleme24  37978  cdleme26ee  37986  cdlemg2idN  38222  cdlemg31c  38325  cdlemk26-3  38532  dihglblem2N  38920  0ellimcdiv  42716
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