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Theorem simp332 1412
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp332 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜓)

Proof of Theorem simp332
StepHypRef Expression
1 simp32 1253 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1130 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  ivthALT  32636  dalemclqjt  35424  dath2  35526  cdlema1N  35580  cdleme26eALTN  36151  cdlemk7u  36660  cdlemk11u  36661  cdlemk12u  36662  cdlemk23-3  36692  cdlemk33N  36699  cdlemk11ta  36719  cdlemk11tc  36735  cdlemk54  36748
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