Can I claim this William's baptism?

[Lindsay]

William and Robert Mills were brothers. All I know about William is that he was born about 1739.

I have Robert's baptism at St Sepulchre, London in 1745 here:
http://search.ancestry.co.uk/iexec?htx=View&r=5538&dbid=1624&iid=31281_A102261-00130&fn=Robert&ln=Mills&st=d&ssrc=&pid=8051818

There are several other children for parents William and Elizabeth Mills at St Sepulchre 1742-1750, but no William.

There is, however, this baptism at St Antholin, Budge Row, London in December 1739 for William MILLES, parents William and Elizabeth:
http://search.ancestry.co.uk/iexec?htx=View&r=5538&dbid=1624&iid=31281_A101026-00196&fn=William&ln=Milles&st=d&ssrc=&pid=5314973

I'd love to claim him, but does it sound reasonable? Unfortunately none of the entries have father's occupation which makes it hard to be sure. I can't see any more baptisms for William and Elizabeth MILLES.

[Shona]

There's a William born to William and Elizabeth in Shadwell, Tower Hamlets, London in 1734.

[kiterunner]

It looks likely, yes. Hard to be sure without more proof, though.

[Shona]

So it looks as if William was their first child. Do you know where William and Elizabeth married? May be he was baptised in her home parish.

[Lindsay]

There's a William born to William and Elizabeth in Shadwell, Tower Hamlets, London in 1734.

I couldn't find a burial for that William. I'd like it to be a different family because if the St Antholin baptism is correct I can tie it in to a marriage for William and Elizabeth 10 months before that gets me back another 2 generations...

It's so easy to get carried away :D:D

[Lindsay]

The marriage I've found is at St Helen's Bishopsgate; he's from St Michael Cornhill, she's from St Botolph Aldgate, so if it's the right family they were really moving around (though being London these places are only a few minutes apart).

I'm not sure there's a way of proving it for sure, other than eliminating other candidates.