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Theorem simp3r2 1262
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 1175 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1115 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 387  w3a 1068
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 388  df-3an 1070
This theorem is referenced by:  nllyrest  21798  cdlemblem  36380  cdleme21  36924  cdleme22b  36928  cdleme40m  37054  cdlemg34  37299  cdlemk5u  37448  cdlemk6u  37449  cdlemk21N  37460  cdlemk20  37461  cdlemk26b-3  37492  cdlemk26-3  37493  cdlemk28-3  37495  cdlemky  37513  cdlemk11t  37533  cdlemkyyN  37549  stoweidlem56  41778
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