let a, b, c, d be set ; :: thesis: ( <*a,b*> = <*c,d*> implies ( a = c & b = d ) )
assume A1:
<*a,b*> = <*c,d*>
; :: thesis: ( a = c & b = d )
thus a =
<*a,b*> . 1
by Th61
.=
c
by A1, Th61
; :: thesis: b = d
thus b =
<*a,b*> . 2
by Th61
.=
d
by A1, Th61
; :: thesis: verum