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Theorem simp132 1409
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp132 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜓)

Proof of Theorem simp132
StepHypRef Expression
1 simp32 1268 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant1 1164 1 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂𝜁) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  ax5seglem3  26168  3atlem1  35504  3atlem2  35505  3atlem5  35508  2llnjaN  35587  4atlem11b  35629  4atlem12b  35632  lplncvrlvol2  35636  dalemtea  35651  dath2  35758  cdlemblem  35814  dalawlem1  35892  lhpexle3lem  36032  4atexlemex6  36095  cdleme22f2  36368  cdleme22g  36369  cdlemg7aN  36646  cdlemg34  36733  cdlemj1  36842  cdlemk23-3  36923  cdlemk25-3  36925  cdlemk26b-3  36926
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