Metamath Proof Explorer


Theorem r1fnon

Description: The cumulative hierarchy of sets function is a function on the class of ordinal numbers. (Contributed by NM, 5-Oct-2003) (Revised by Mario Carneiro, 10-Sep-2013)

Ref Expression
Assertion r1fnon
|- R1 Fn On

Proof

Step Hyp Ref Expression
1 rdgfnon
 |-  rec ( ( x e. _V |-> ~P x ) , (/) ) Fn On
2 df-r1
 |-  R1 = rec ( ( x e. _V |-> ~P x ) , (/) )
3 2 fneq1i
 |-  ( R1 Fn On <-> rec ( ( x e. _V |-> ~P x ) , (/) ) Fn On )
4 1 3 mpbir
 |-  R1 Fn On