Definition df-k2

Description: Define a function that takes an ordinal and returns the second argument of the ordered triple <. x , y , n >. such that the ordinal equals ( J<. x , y , n >. ) . Based on the second case of Definition 15.7 of TakeutiZaring p. 156. (Contributed by BTernaryTau, 2-Sep-2026)

	Ref	Expression
Assertion	df-k2	Could not format assertion : No typesetting found for |- _K2 = { <. z , y >. | ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) } with typecode |-

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		ck2	Could not format _K2 : No typesetting found for class _K2 with typecode class
1		vz	$$setvarz$$
2		vy	$$setvary$$
3	2	cv	$$setvary$$
4		con0	$$class\mathrm{On}$$
5	3 4	wcel	$$wffy\in \mathrm{On}$$
6		vn	$$setvarn$$
7		c9o	Could not format 9o : No typesetting found for class 9o with typecode class
8		vx	$$setvarx$$
9	1	cv	$$setvarz$$
10		cj	Could not format _J : No typesetting found for class _J with typecode class
11	8	cv	$$setvarx$$
12	6	cv	$$setvarn$$
13	11 3 12	cotp	$$class⟨x,y,n⟩$$
14	13 10	cfv	Could not format ( _J ` <. x , y , n >. ) : No typesetting found for class ( _J ` <. x , y , n >. ) with typecode class
15	9 14	wceq	Could not format z = ( _J ` <. x , y , n >. ) : No typesetting found for wff z = ( _J ` <. x , y , n >. ) with typecode wff
16	15 8 4	wrex	Could not format E. x e. On z = ( _J ` <. x , y , n >. ) : No typesetting found for wff E. x e. On z = ( _J ` <. x , y , n >. ) with typecode wff
17	16 6 7	wrex	Could not format E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) : No typesetting found for wff E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) with typecode wff
18	5 17	wa	Could not format ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) : No typesetting found for wff ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) with typecode wff
19	18 1 2	copab	Could not format { <. z , y >. | ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) } : No typesetting found for class { <. z , y >. | ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) } with typecode class
20	0 19	wceq	Could not format _K2 = { <. z , y >. | ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) } : No typesetting found for wff _K2 = { <. z , y >. | ( y e. On /\ E. n e. 9o E. x e. On z = ( _J ` <. x , y , n >. ) ) } with typecode wff