metamath/valid/amc12-2000-p11.mm

${
  amc12-2000-p11.0 $e |- ( ph -> A e. RR ) $.
  amc12-2000-p11.1 $e |- ( ph -> B e. RR ) $.
  amc12-2000-p11.2 $e |- ( ph -> A =/= 0 ) $.
  amc12-2000-p11.3 $e |- ( ph -> B =/= 0 ) $.
  amc12-2000-p11.4 $e |- ( ph -> ( A x. B ) = ( A - B ) ) $.
  $( (Contributed by Stanislas Polu, 26-Oct-2020.) $)
  amc12-2000-p11 $p |- ( ph -> ( ( ( A / B ) + ( B / A ) ) - ( A x. B ) ) = 2 ) 
$=
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recnd cc wcel wne divcan1 syl3anc sqcld divdird addcld divsubdird binom2sub 
wceq syl2anc 2cnd subcld sub32d subsub4d addsubassd addid1d subsubd addid2d 
subidd ) ABCIJZCBIJZKJZBCLJZMJBNOJZVQIJZCNOJZVQIJZKJZVQNOJZVQIJZMJZNAVPWBVQ 
WDMAVNVSVOWAKAVNVNBLJBIJZVSAWFVNAVNBABCABDULZACEULZGUBZWGFUCPAWFVNBBIJLJZVS 
AVNBBWIWGWGFUDAWJBBLJZVQIJZVSAWJWKCBLJZIJWLABCBBWGWHWGWGGFUAAWMVQWKIACBWHWG 
UEQRAVRWKVQIABWGUFSUGRRAVOVOCLJCIJZWAAWNVOAVOCACBWHWGFUBZWHGUCPAWNVOCCIJLJZ 
WAAVOCCWOWHWHGUDAWPCCLJZVQIJWAACBCCWHWGWHWHFGUAAWQVTVQIAVTWQACWHUFPSRRRUHAW 
DVQAWDVQVQLJZVQIJZVQAWCWRVQIAVQABCWGWHUIZUFSAWSVQVQIJVQLJZVQAVQVQVQWTWTWTAB 
CWGWHFGUJZUKAVQUMUNZXCVQTUOXAVQVCWTWTXBVQVQUPUQRRPUHAWEVRVTKJZVQIJZWDMJZNAW 
BXEWDMAXEWBAVRVTVQABWGURZACWHURZWTXBUSPSAXFXDWCMJZVQIJZNAXJXFAXDWCVQAVRVTXG 
XHUTZAVQWTURWTXBVAPAXJXDBCMJZNOJZMJZVQIJZNAXIXNVQIAWCXMXDMAVQXLNOHSQSAXOXDV 
RNVQLJZMJZVTKJZMJZVQIJZNAXNXSVQIAXMXRXDMABUMUNCUMUNXMXRVCWGWHBCVBVDQSAXTXDV 
TMJZXQMJZVQIJZNAXSYBVQIAYBXSAYBXDXQMJVTMJXSAXDVTXQXKXHAVRXPXGANVQAVEZWTUIZV 
FZVGAXDXQVTXKYFXHVHRPSAYCVRVTVTMJZKJZXQMJZVQIJZNAYBYIVQIAYAYHXQMAVRVTVTXGXH 
XHVISSAYJVRXQMJZVQIJZNAYIYKVQIAYHVRXQMAYHVRTKJVRAYGTVRKAVTXHVMQAVRXGVJRSSAY 
LVRVRMJZXPKJZVQIJZNAYKYNVQIAVRVRXPXGXGYEVKSAYOXPVQIJNAYNXPVQIAYNTXPKJXPAYMT 
XPKAVRXGVMSAXPYEVLRSANVQYDWTXBUCRRRRRRRRRR $.
$}