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Theorem simp331 1328
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp331 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)

Proof of Theorem simp331
StepHypRef Expression
1 simp31 1211 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant3 1137 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1089
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 210  df-an 400  df-3an 1091
This theorem is referenced by:  ivthALT  34266  dalemclpjs  37390  dath2  37493  cdlema1N  37547  cdlemk7u  38626  cdlemk11u  38627  cdlemk12u  38628  cdlemk22  38649  cdlemk23-3  38658  cdlemk24-3  38659  cdlemk33N  38665  cdlemk11ta  38685  cdlemk11tc  38701  cdlemk54  38714
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