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Metamath Proof Explorer

Theorem dfsucmap4

Description: Alternate definition of the successor map. (Contributed by Peter Mazsa, 28-Jan-2026)

Ref Expression
Assertion dfsucmap4 Could not format assertion : No typesetting found for |- SucMap = ( m e. _V |-> suc m ) with typecode |-

Proof

Step Hyp Ref Expression
1 eqcom ⊢ n = suc ⁡ m ↔ suc ⁡ m = n
2 1 opabbii ⊢ m n | n = suc ⁡ m = m n | suc ⁡ m = n
3 mptv ⊢ m ∈ V ⟼ suc ⁡ m = m n | n = suc ⁡ m
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 2 3 4 3eqtr4ri Could not format SucMap = ( m e. _V |-> suc m ) : No typesetting found for |- SucMap = ( m e. _V |-> suc m ) with typecode |-