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Theorem simp2l2 1269
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 1188 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
213ad2ant2 1130 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by:  btwnconn1lem9  33558  btwnconn1lem10  33559  btwnconn1lem11  33560  btwnconn1lem12  33561  2lplnja  36757  cdlemk21-2N  38029  cdlemk31  38034  cdlemk19xlem  38080  jm2.27  39612
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