TNT (thing)

example proof

1: Va:(a+0)=a
2nd axiom
2: (S0+0)=S0
specification (1)
3: S0=(S0+0)
symmetry (2)
4: S0=S0
transitivity (4,3)
5: 0=0
successorship (4)
QED

This is a simple TNT proof that zero is equal to itself.