let x be set ; :: thesis: ( x U+ {} = [:x,{1}:] & {} U+ x = [:x,{2}:] )
thus x U+ {} =
[:x,{1}:] \/ [:{} ,{2}:]
by Th74
.=
[:x,{1}:] \/ {}
by ZFMISC_1:113
.=
[:x,{1}:]
; :: thesis: {} U+ x = [:x,{2}:]
thus {} U+ x =
[:{} ,{1}:] \/ [:x,{2}:]
by Th74
.=
{} \/ [:x,{2}:]
by ZFMISC_1:113
.=
[:x,{2}:]
; :: thesis: verum