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Theorem simp2l2 1373
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp2l2 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)

Proof of Theorem simp2l2
StepHypRef Expression
1 simpl2 1245 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
213ad2ant2 1165 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385  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:  btwnconn1lem9  32707  btwnconn1lem10  32708  btwnconn1lem11  32709  btwnconn1lem12  32710  2lplnja  35632  cdlemk21-2N  36904  cdlemk31  36909  cdlemk19xlem  36955  jm2.27  38348
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