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The allegation which led me to ask for sources was:
What the Catholic church teaches is that there is one body and an that to be a member of that body is to be saved.

The controversial part (to me) was that to be a member of that body is to be saved.

This could be expressed as IF you are a member of this body THEN you are saved -- Or -- every member of the set of members of the body is a member of the set of saved people.

Now when I look at the quotes you provide, i do not see that. I see at most IF you are NOT a member of the body, then you are NOT saved -- Or -- every member of the set of people NOT members of the body is also a member of the set NOT saved people.

These two propositions are not identical.

For: Let's play with squares and rectangles.
IF you are a square, you are a rectangle.
BUT that is NOT the same as
If you are NOT a square, you are not a rectangle.

So, looking at the logic, Saying "if you are not in the body you are not saved"
is NOT the same as saying
If you are in the body you are saved.

So the quotes you provided do not support your contention.
QED

So, looking at the logic, Saying "if you are not in the body you are not saved" is NOT the same as saying If you are in the body you are saved.

I like logic problems like this. :) So, are you saying that they are different because the first does not imply the second? That is, the first leaves room for the possibility that some who are in the body are nevertheless not saved, whereas the second precludes this possibility.

These two propositions are not identical.
For: Let's play with squares and rectangles.
IF you are a square, you are a rectangle.
BUT that is NOT the same as
If you are NOT a square, you are not a rectangle.
So, looking at the logic, Saying "if you are not in the
body you are not saved"
is NOT the same as saying
If you are in the body you are saved.

So the quotes you provided do not support your contention.

What a mumble-jumble of logic! Come on, you can do better than that :-)