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Theorem simp111 1301
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 1202 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜑)
213ad2ant1 1132 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  tsmsxp  24179  ps-2b  39465  llncvrlpln2  39540  4atlem11b  39591  4atlem12b  39594  lplncvrlvol2  39598  lneq2at  39761  2lnat  39767  cdlemblem  39776  4atexlemex6  40057  cdleme24  40335  cdleme26ee  40343  cdlemg2idN  40579  cdlemg31c  40682  cdlemk26-3  40889  0ellimcdiv  45605
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