let C be Category; :: thesis: for a being Object of C
for m being Morphism of (C -SliceCat a) holds
( m = [[(m `11),(m `12)],(m `2)] & dom (m `12) = cod (m `2) & m `11 = (m `12) (*) (m `2) & dom m = m `11 & cod m = m `12 )
let o be Object of C; :: thesis: for m being Morphism of (C -SliceCat o) holds
( m = [[(m `11),(m `12)],(m `2)] & dom (m `12) = cod (m `2) & m `11 = (m `12) (*) (m `2) & dom m = m `11 & cod m = m `12 )
let m be Morphism of (C -SliceCat o); :: thesis: ( m = [[(m `11),(m `12)],(m `2)] & dom (m `12) = cod (m `2) & m `11 = (m `12) (*) (m `2) & dom m = m `11 & cod m = m `12 )
consider a, b being Element of Hom o, f being Morphism of C such that
A1: m = [[a,b],f] and
A2: dom b = cod f and
A3: a = b (*) f by Def11;
A4: m `11 = a by A1, MCART_1:85;
m `12 = b by A1, MCART_1:85;
hence ( m = [[(m `11),(m `12)],(m `2)] & dom (m `12) = cod (m `2) & m `11 = (m `12) (*) (m `2) & dom m = m `11 & cod m = m `12 ) by A1, A2, A3, A4, Th2; :: thesis: verum