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Theorem simp3l3 1161
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3l3 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)

Proof of Theorem simp3l3
StepHypRef Expression
1 simpl3 1059 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
213ad2ant3 1077 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  cvmlift2lem10  30548  cdleme36m  34767  cdlemk5u  35167  cdlemk21N  35179  cdlemk20  35180  cdlemk27-3  35213  cdlemk28-3  35214  dihmeetlem20N  35633
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