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Theorem simp333 1412
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp333 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simp333
StepHypRef Expression
1 simp33 1253 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1129 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1071
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 383  df-3an 1073
This theorem is referenced by:  ivthALT  32667  dalemclrju  35444  dath2  35545  cdlema1N  35599  cdleme26eALTN  36170  cdlemk7u  36679  cdlemk11u  36680  cdlemk12u  36681  cdlemk22  36702  cdlemk23-3  36711  cdlemk33N  36718  cdlemk11ta  36738  cdlemk11tc  36754  cdlemk54  36767
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