Theorem dfpre3

Description: Alternate definition of the successor-predecessor. (Contributed by Peter Mazsa, 12-Jan-2026)

	Ref	Expression
Assertion	dfpre3	Could not format assertion : No typesetting found for |- ( N e. V -> pre N = ( iota m suc m = N ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		dfpre2	Could not format ( N e. V -> pre N = ( iota m m SucMap N ) ) : No typesetting found for |- ( N e. V -> pre N = ( iota m m SucMap N ) ) with typecode |-
2		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 |-
3	2	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 |-
4	3	iotabidv	Could not format ( N e. V -> ( iota m m SucMap N ) = ( iota m suc m = N ) ) : No typesetting found for |- ( N e. V -> ( iota m m SucMap N ) = ( iota m suc m = N ) ) with typecode |-
5	1 4	eqtrd	Could not format ( N e. V -> pre N = ( iota m suc m = N ) ) : No typesetting found for |- ( N e. V -> pre N = ( iota m suc m = N ) ) with typecode |-