You can export your iPhone contacts by logging into your iCloud account.
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First, you’ll need to enable iCloud on your iPhone or just double-check that contacts are already being synced with iCloud. (in your phone settings, click into iCloud and make sure Contacts is enabled)
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On your computer, open a new browser page and navigate to icloud.com and log into your iCloud account
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Click into the Contacts icon where you should then see all of your contacts from your phone
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Click on the first Contact's name and then Ctrl+A which should select ALL contacts
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While all contacts are selected, click the gear icon in the lower left side of the page and select Export vCard