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Metamath Proof Explorer

Theorem dfsuccl2

Description: Alternate definition of the class of all successors. (Contributed by Peter Mazsa, 29-Jan-2026)

Ref Expression
Assertion dfsuccl2 Could not format assertion : No typesetting found for |- Suc = { n | E. m suc m = 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 df-sucmap Could not format SucMap = { <. m , n >. | suc m = n } : No typesetting found for |- SucMap = { <. m , n >. | suc m = n } with typecode |-
3 2 rneqi Could not format ran SucMap = ran { <. m , n >. | suc m = n } : No typesetting found for |- ran SucMap = ran { <. m , n >. | suc m = n } with typecode |-
4 rnopab ⊢ ran ⁡ m n | suc ⁡ m = n = n | ∃ m suc ⁡ m = n
5 1 3 4 3eqtri Could not format Suc = { n | E. m suc m = n } : No typesetting found for |- Suc = { n | E. m suc m = n } with typecode |-