"So we're leaving the hospital after six, seven days", Serena says later in the video, while holding her baby.
Serena hinted at a hard birth, saying: 'We had a lot of complications, but look who we got!'
'Alexis supposes we're having a kid, yet I have a solid doubt that it's a young lady, ' said Serena.
What do you think about naming a baby girl after her father?
As the tail end of the video puts it, Baby Ohanian was born September 1, at 6 pounds 14 ounces, "Grand Slam titles: 1".More news: Hurricane Irma looting: Caribbean Chaos as prisoners escape and looters run riot
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"I knew it was coming", she said.
Her Instagram post has attracted more than 270,000 likes within an hour of posting and her tweet was retweeted more than 1,300 times (at time of writing). It's also acknowledgement of Williams, who has earned four Olympic gold medals. We also see a little dancing, some obvious adoration between the tennis pro and her fiancé, and finally the lovely Alexis.
And that's true. No one had any clue Williams was pregnant until she accidentally posted a Snapchat in a yellow one-piece swimsuit with the caption: "20 weeks". "I told her: 'You come if you're ready.' And I will do everything for her to be ready for Australia".
Williams' 23 major titles are a record for the professional era, which began in 1968; she broke a tie with Steffi Graf in Australia this year. She is both a tennis player and a mother, and she has to deal with both of them.