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Theorem simp3l1 1378
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 1243 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) → 𝜑)
213ad2ant3 1166 1 ((𝜏𝜂 ∧ ((𝜑𝜓𝜒) ∧ 𝜃)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  cvmlift2lem10  31803  cdleme26ee  36373  cdleme36m  36474  cdleme40m  36480  cdlemg18b  36692  cdlemk5u  36874  cdlemk6u  36875  cdlemk21N  36886  cdlemk20  36887  cdlemk27-3  36920  cdlemk28-3  36921  dihmeetlem20N  37339
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