I am gaving trouble proving a natural deduction proof when there is no predicate given. Only conclusion is given. I understand the rules of elimnations, inclusions, IPs and others but I having trouble applying them when no predicate is given. The question is: $$ \vdash P(a) \to \forall x(P(x) \lor \lnot(x = a))$$
Also can anyone suggest me good websites to check my proofs and practice them. I usually use https://proofs.openlogicproject.org but in this question it is showing that its not well formed.
