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Theorem simp3l1 1272
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3l1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)

Proof of Theorem simp3l1
StepHypRef Expression
1 simpl1 1185 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant3 1129 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1081
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 1083
This theorem is referenced by:  cvmlift2lem10  32547  cdleme26ee  37478  cdleme36m  37579  cdleme40m  37585  cdlemg18b  37797  cdlemk5u  37979  cdlemk6u  37980  cdlemk21N  37991  cdlemk20  37992  cdlemk27-3  38025  cdlemk28-3  38026  dihmeetlem20N  38444
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