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Metamath Proof Explorer

Theorem brsucmap

Description: Binary relation form of the successor map, general version. (Contributed by Peter Mazsa, 6-Jan-2026)

Ref Expression
Assertion brsucmap Could not format assertion : No typesetting found for |- ( ( M e. V /\ N e. W ) -> ( M SucMap N <-> suc M = N ) ) with typecode |-

Proof

Step Hyp Ref Expression
1 suceq ⊢ m = M → suc ⁡ m = suc ⁡ M
2 id ⊢ n = N → n = N
3 1 2 eqeqan12d ⊢ m = M ∧ n = N → suc ⁡ m = n ↔ suc ⁡ M = N
4 df-sucmap Could not format SucMap = { <. m , n >. | suc m = n } : No typesetting found for |- SucMap = { <. m , n >. | suc m = n } with typecode |-
5 3 4 brabga Could not format ( ( M e. V /\ N e. W ) -> ( M SucMap N <-> suc M = N ) ) : No typesetting found for |- ( ( M e. V /\ N e. W ) -> ( M SucMap N <-> suc M = N ) ) with typecode |-