let
p
,
q
,
r
be
boolean
object
;
:: thesis:
(
p
=>
q
=
TRUE
&
q
=>
r
=
TRUE
implies
p
=>
r
=
TRUE
)
(
p
=
FALSE
or
p
=
TRUE
)
by
Def3
;
hence
(
p
=>
q
=
TRUE
&
q
=>
r
=
TRUE
implies
p
=>
r
=
TRUE
) ;
:: thesis:
verum