I recently got inspired by the famous proof- All Horses are the Same Color©. I soon learned that the proof has flaws- namely, the Induction hypothesis fails at n=2. So, after much thought, I came up with my own foolproof version.

Theorem: All people are virgins

Proof: 

1. Base case (n=1) Suppose only a single person (P1) exists. We know only one person cannot have sex with himself/herself, therefore P1 is a virgin.
2. n=2. Now suppose we add another person, P2. Now, P2 may or may not be a virgin. However, if P2 is not a virgin, the only person he/she could have had sex with is P1. Hence P1 is also not a virgin. We know this is false (see step 1). Therefore, P2 is also a virgin.
3. n=3 Another person, P3 is added. Same as above, if P3 is not virgin, atleast one of P1 or P2 must not be virgin. We know this is false (step 2). Therefore P3 is virgin.
...

Induction hypothesis: Suppose a group of n people are virgins.

Inductive step:  

We want to show that n+1 people are all virgins
Again, if we take a group of n people and add one person, the only way the (n+1)th person would be a virgin is if one of the n people already in the group is not a virgin. We know from this is false since the IH states all n people are virgins. Therefore, the (n+1)th person must be a virgin.

Therefore, all people are virgins. Q.E.D.

Can anyone find the error in my proof?