metamath/valid/algebra-manipexpr-2erprsqpesqeqnrpnesq.mm (14 lines of code) (raw):

${ algebra-manipexpr-2erprsqpesqeqnrpnesq.0 $e |- ( ph -> E e. CC ) $. algebra-manipexpr-2erprsqpesqeqnrpnesq.1 $e |- ( ph -> R e. CC ) $. $( (Contributed by Stanislas Polu, 8-Oct-2020.) $) algebra-manipexpr-2erprsqpesqeqnrpnesq $p |- ( ph -> ( ( 2 x. ( E x. R ) ) + ( ( E ^ 2 ) + ( R ^ 2 ) ) ) = ( ( -u R + -u E ) ^ 2 ) ) $= ( c2 cmul co cexp caddc cneg cc wcel wceq sqneg oveq2d oveq12d sqcld mulcld syl mul2negd 2cnd add32d addcomd mulcomd addcld eqtr4d eqtr2d negcld binom2 eqtrd syl2anc eqcomd ) AFCBGHZGHZCFIHZBFIHZJHZJHZBKZFIHZFUTCKZGHZGHZJHZVBFI HZJHZUTVBJHFIHZAVGUQFBCGHZGHZJHZUPJHZUSAVEVKVFUPJAVAUQVDVJJABLMVAUQNEBOTAVC VIFGABCEDUAPQACLMVFUPNDCOTQAVLUQUPJHZVJJHZUSAUQVJUPABERZAFVIAUBZABCEDSSACDR ZUCAVNURUOJHUSAVMURVJUOJAUQUPVOVQUDAVIUNFGABCEDUEPQAUOURAFUNVPACBDESSAUPUQV QVOUFUDUGUKUHAVHVGAUTLMVBLMVHVGNABEUIACDUIUTVBUJULUMUK $. $}