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Theorem simp2l2 1272
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 1191 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜓)
213ad2ant2 1133 1 ((𝜏 ∧ ((𝜑𝜓𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  poxp3  8174  btwnconn1lem9  36077  btwnconn1lem10  36078  btwnconn1lem11  36079  btwnconn1lem12  36080  2lplnja  39602  cdlemk21-2N  40874  cdlemk31  40879  cdlemk19xlem  40925  jm2.27  42997
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