let D be non empty set ; :: thesis: for d being Element of D
for F being BinOp of D st F is associative & F is having_a_unity & F is having_an_inverseOp holds
(F * (id D),(the_inverseOp_wrt F)) . d,d = the_unity_wrt F
let d be Element of D; :: thesis: for F being BinOp of D st F is associative & F is having_a_unity & F is having_an_inverseOp holds
(F * (id D),(the_inverseOp_wrt F)) . d,d = the_unity_wrt F
let F be BinOp of D; :: thesis: ( F is associative & F is having_a_unity & F is having_an_inverseOp implies (F * (id D),(the_inverseOp_wrt F)) . d,d = the_unity_wrt F )
assume A1: ( F is associative & F is having_a_unity & F is having_an_inverseOp ) ; :: thesis: (F * (id D),(the_inverseOp_wrt F)) . d,d = the_unity_wrt F
set u = the_inverseOp_wrt F;
thus (F * (id D),(the_inverseOp_wrt F)) . d,d = F . d,((the_inverseOp_wrt F) . d) by Th87
.= the_unity_wrt F by A1, Th63 ; :: thesis: verum