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Theorem simp332 1207
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 1090 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1076 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  ivthALT  31306  dalemclqjt  33742  dath2  33844  cdlema1N  33898  cdleme26eALTN  34470  cdlemk7u  34979  cdlemk11u  34980  cdlemk12u  34981  cdlemk23-3  35011  cdlemk33N  35018  cdlemk11ta  35038  cdlemk11tc  35054  cdlemk54  35067
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