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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 1087
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 1089
This theorem is referenced by:  axcontlem4  28982  ps-2b  39484  llncvrlpln2  39559  4atlem11b  39610  4atlem12b  39613  2lnat  39786  cdlemblem  39795  4atexlemex6  40076  cdleme24  40354  cdleme26ee  40362  cdlemg2idN  40598  cdlemg31c  40701  cdlemk26-3  40908  dihglblem2N  41296  0ellimcdiv  45664
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