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Theorem simp112 1211
 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 1112 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant1 1102 1 ((((𝜑𝜓𝜒) ∧ 𝜃𝜏) ∧ 𝜂𝜁) → 𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1054 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 385  df-3an 1056 This theorem is referenced by:  axcontlem4  25892  ps-2b  35086  llncvrlpln2  35161  4atlem11b  35212  4atlem12b  35215  2lnat  35388  cdlemblem  35397  4atexlemex6  35678  cdleme24  35957  cdleme26ee  35965  cdlemg2idN  36201  cdlemg31c  36304  cdlemk26-3  36511  dihglblem2N  36900  0ellimcdiv  40199
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