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Metamath Proof Explorer

Theorem eupre

Description: Unique predecessor exists on the successor class. (Contributed by Peter Mazsa, 27-Jan-2026)

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

Proof

Step Hyp Ref Expression
1 df-succl Could not format Suc = ran SucMap : No typesetting found for |- Suc = ran SucMap with typecode |-
2 1 eleq2i Could not format ( N e. Suc <-> N e. ran SucMap ) : No typesetting found for |- ( N e. Suc <-> N e. ran SucMap ) with typecode |-
3 eupre2 Could not format ( N e. V -> ( N e. ran SucMap <-> E! m m SucMap N ) ) : No typesetting found for |- ( N e. V -> ( N e. ran SucMap <-> E! m m SucMap N ) ) with typecode |-
4 2 3 bitrid Could not format ( N e. V -> ( N e. Suc <-> E! m m SucMap N ) ) : No typesetting found for |- ( N e. V -> ( N e. Suc <-> E! m m SucMap N ) ) with typecode |-