I need help with this proof for my philosophy class. This proof is supposed to be done via conditional proof, so it is supposed to use ACP and CP to derive the conclusion! This is an assignment that is submitted through Aplia, so I need it to be precise and the assignment is due tonight, so I would like it done before tonight please!

This is the key:
The * = dot
The > = horseshoe
The v = wedge
The ≡ = triple bar
The ~ = tilde
The statement after the / (slash) is the conclusion that I need.
The first one is:
1. (F * H) ≡ H
2. F>G
/ F≡ H

Sure, I'd be happy to help you with your proof! To prove the conclusion F ≡ H using a conditional proof, we'll start by assuming F as a temporary assumption and aim to derive H from it. Here's how we can proceed:

1. (F * H) ≡ H (Premise)
2. F > G (Premise)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
3. F (Assumption)
4. (F * H) (1, 3, ≡E)
5. H (4, *E)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
6. F > H (3-5, >I)
7. H v ~H (Tautology)
8. F v ~H (6, 7, ≡E)
9. ~H > F (8, >I)
10. ~H v F (9, CP)
11. H ≡ F (10, 7, ≡I)
12. F ≡ H (11, ≡E)

By assuming F and using the material implication (→) introduction and elimination rules, we have shown that F ≡ H. Now you can complete the rest of your proof by using a similar approach to derive F > H. I hope this helps you complete your assignment! Let me know if you have any further questions.