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Theorem simp3l3 1277
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 1190 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜒)
213ad2ant3 1132 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1084
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 210  df-an 400  df-3an 1086
This theorem is referenced by:  cvmlift2lem10  32616  cdleme36m  37702  cdlemk5u  38102  cdlemk21N  38114  cdlemk20  38115  cdlemk27-3  38148  cdlemk28-3  38149  dihmeetlem20N  38567
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