Thanks, Konrad! I see that the HOL light BOOL_CASES_AX is proved in class.ml 
using the result I mentioned, EXCLUDED_MIDDLE,  which class.ml says is derived 
from Beeson's book: 

let BOOL_CASES_AX = prove
 (`!t. (t <=> T) \/ (t <=> F)`,
  GEN_TAC THEN DISJ_CASES_TAC(SPEC `t:bool` EXCLUDED_MIDDLE) THEN
  ASM_REWRITE_TAC[]);;

-- 
Best,
Bill 

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