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Theorem simp3r2 1281
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r2 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Proof of Theorem simp3r2
StepHypRef Expression
1 simpr2 1194 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1134 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  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 206  df-an 397  df-3an 1088
This theorem is referenced by:  nllyrest  22743  cdlemblem  38069  cdleme21  38613  cdleme22b  38617  cdleme40m  38743  cdlemg34  38988  cdlemk5u  39137  cdlemk6u  39138  cdlemk21N  39149  cdlemk20  39150  cdlemk26b-3  39181  cdlemk26-3  39182  cdlemk28-3  39184  cdlemky  39202  cdlemk11t  39222  cdlemkyyN  39238  stoweidlem56  43941
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