When I had 7 cards in my hand, I attacked with a Digimon with this card in its digivolution cards, and <Draw 1> activated from a [When Attacking] effect. I now have 8 cards, so does that attack perform a security check with this card's inherited effect of <Security Attack +1>?
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Official Ruling
Yes. The inherited effect activates as soon as you have 8 cards in your hand, so the Digimon gets <Security Attack +1> for the rest of the attack.
Source: ST8-08 AeroVeedramon