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Theorem simp3r2 1319
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 1212 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1127 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1072
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 385  df-3an 1074
This theorem is referenced by:  nllyrest  21412  cdlemblem  35499  cdleme21  36044  cdleme22b  36048  cdleme40m  36174  cdlemg34  36419  cdlemk5u  36568  cdlemk6u  36569  cdlemk21N  36580  cdlemk20  36581  cdlemk26b-3  36612  cdlemk26-3  36613  cdlemk28-3  36615  cdlemky  36633  cdlemk11t  36653  cdlemkyyN  36669  stoweidlem56  40693
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