I saw one guy produce a proof that Joe is a squid. His proof is 10 lines long but I can do it 8. He infers from his proof that the argument is valid, even though you can prove using his same method that Joe is not a squid in 3 lines. Yet, he persists. He exhibited what he thinks is a proof and that's it. His method is flawed but he doesn't know that and he certainly doesn't understand why it is flawed. Using apparently the same method, I proved correctly the argument not valid:

*Proof*

*An elephant is not a squid..............P3*

Joe is an elephant...........................P5

Therefore, Joe is a not squid..........P3, P5, R1: ((x ≠ y) ∧ (z = x) ) → (z ≠ y)

Which is basically what you said.

Formally, for the argument to be valid, since equality is not a logical symbol, you need to add a premise with the R1 rule

*((x ≠ y) ∧ (z = x) ) → (z ≠ y)*. But it's implicit anyway.

EB