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Theorem simp111 1188
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp111 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)

Proof of Theorem simp111
StepHypRef Expression
1 simp11 1089 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant1 1080 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1036 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 197  df-an 386  df-3an 1038 This theorem is referenced by:  tsmsxp  21939  ps-2b  34587  llncvrlpln2  34662  4atlem11b  34713  4atlem12b  34716  lplncvrlvol2  34720  lneq2at  34883  2lnat  34889  cdlemblem  34898  4atexlemex6  35179  cdleme24  35459  cdleme26ee  35467  cdlemg2idN  35703  cdlemg31c  35806  cdlemk26-3  36013  0ellimcdiv  39681
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