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Theorem simp3r1 1167
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Proof of Theorem simp3r1
StepHypRef Expression
1 simpr1 1065 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1082 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 197  df-an 386  df-3an 1038
This theorem is referenced by:  nllyrest  21212  segletr  31898  cdlemblem  34594  cdleme21  35140  cdleme22b  35144  cdleme40m  35270  cdlemg34  35515  cdlemk5u  35664  cdlemk6u  35665  cdlemk21N  35676  cdlemk20  35677  cdlemk26b-3  35708  cdlemk26-3  35709  cdlemk28-3  35711  cdlemk37  35717  cdlemky  35729  cdlemk11t  35749  cdlemkyyN  35765  dihmeetlem20N  36130  stoweidlem56  39606
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