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Theorem simp2l2 1265
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 1184 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
213ad2ant2 1126 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by:  btwnconn1lem9  33453  btwnconn1lem10  33454  btwnconn1lem11  33455  btwnconn1lem12  33456  2lplnja  36635  cdlemk21-2N  37907  cdlemk31  37912  cdlemk19xlem  37958  jm2.27  39483
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