This is almost impossible to explain to a novice who is most liable to suspect mockery. But search this site for, say, Bertran Russell. One of the pages (https://www.cut-the-knot.org/selfreference/russell.shtml) shows his and Whitehead's proof of 1+1=2.
The fact is that a proof, if any is needed, depends on the definition of the symbols 1, +, =, 2. It could be that no proof is needed if you define 2 appropriately.