In the Greek, does 1 Corinthians 5:7 say Jesus is our Passover Lamb?

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A friend of mine recently saw a teaching, where it was claimed that in Greek, 1 Corinthians does not say “Passover lamb”. I’ve copied and pasted his comment below. Since I don’t know Greek, I don’t have a response for him. I’m hoping someone can help.

Paul actually says, "christ was slain/killed, pesach is ours". The
word "lamb", or "for us" is not even in the original Greek
translation. Purge out the old leaven on his behalf!

It should read as follows directly from the Greek Codex Sinaiticus…

⁷ μα ζυμοι εκκα θαρατε ┬ την παλαι αν ζυμην ϊνα η τε νεον φυραμα καθωϲ εϲτε αζυ μοι και γαρ το παϲχα η μων ┬ ετυθη χϲ

⁸ ωϲτε εορταζω μεν μη εν ζυμη παλαια μηδε εν ζυμη κακιαϲ και
πονηριαϲ αλλ εν α ζυμοιϲ ειλικρινι αϲ και αληθιαϲ

Therefore Purge out the old leaven, that you may be a new lump, since you truly are unleavened. And the truth is Pesach is ours, Mashiach was killed.

1 Corinthians 5:7, 8
⁷ Get rid of the yeast of that which contains leavening agents so that we might be as a new batch of dough, and as much as we
shall become like unleavened bread. ⁸ And the truth is, the
Festival of Pesach is ours Mashiach was killed. Thus we shall
celebrate the festival, not by way of old leaven, nor by way of the
leaven of vindictiveness and immorality, but on account of the
unleavened bread of sincerity and truthfulness.