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Theorem simp3r3 1282
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r3 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simp3r3
StepHypRef Expression
1 simpr3 1195 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1134 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  hash7g  14522  nllyrest  23510  cdlemblem  39776  cdleme21  40320  cdleme22b  40324  cdleme40m  40450  cdlemg34  40695  cdlemk5u  40844  cdlemk6u  40845  cdlemk21N  40856  cdlemk20  40857  cdlemk26b-3  40888  cdlemk26-3  40889  cdlemk28-3  40891  cdlemky  40909  cdlemk11t  40929  cdlemkyyN  40945  dihmeetlem20N  41309  stoweidlem56  46012
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