Theorem exeupre

Description: Whenever a predecessor exists, it exists alone. (Contributed by Peter Mazsa, 12-Jan-2026)

	Ref	Expression
Assertion	exeupre	Could not format assertion : No typesetting found for |- ( N e. V -> ( E. m m SucMap N <-> E! m m SucMap N ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		brsucmap	Could not format ( ( m e. _V /\ N e. V ) -> ( m SucMap N <-> suc m = N ) ) : No typesetting found for |- ( ( m e. _V /\ N e. V ) -> ( m SucMap N <-> suc m = N ) ) with typecode |-
2	1	el2v1	Could not format ( N e. V -> ( m SucMap N <-> suc m = N ) ) : No typesetting found for |- ( N e. V -> ( m SucMap N <-> suc m = N ) ) with typecode |-
3	2	exbidv	Could not format ( N e. V -> ( E. m m SucMap N <-> E. m suc m = N ) ) : No typesetting found for |- ( N e. V -> ( E. m m SucMap N <-> E. m suc m = N ) ) with typecode |-
4		exeupre2	$$⊢\exists m\mathrm{suc}m=N\leftrightarrow \exists !m\mathrm{suc}m=N$$
5	3 4	bitrdi	Could not format ( N e. V -> ( E. m m SucMap N <-> E! m suc m = N ) ) : No typesetting found for |- ( N e. V -> ( E. m m SucMap N <-> E! m suc m = N ) ) with typecode |-
6	2	eubidv	Could not format ( N e. V -> ( E! m m SucMap N <-> E! m suc m = N ) ) : No typesetting found for |- ( N e. V -> ( E! m m SucMap N <-> E! m suc m = N ) ) with typecode |-
7	5 6	bitr4d	Could not format ( N e. V -> ( E. m m SucMap N <-> E! m m SucMap N ) ) : No typesetting found for |- ( N e. V -> ( E. m m SucMap N <-> E! m m SucMap N ) ) with typecode |-