let H be ZF-formula; :: thesis: for x, y being Variable holds variables_in (Ex x,y,H) = (variables_in H) \/ {x,y}
let x, y be Variable; :: thesis: variables_in (Ex x,y,H) = (variables_in H) \/ {x,y}
thus variables_in (Ex x,y,H) =
(variables_in (Ex y,H)) \/ {x}
by Th159
.=
((variables_in H) \/ {y}) \/ {x}
by Th159
.=
(variables_in H) \/ ({y} \/ {x})
by XBOOLE_1:4
.=
(variables_in H) \/ {x,y}
by ENUMSET1:41
; :: thesis: verum