Metamath Proof Explorer

Theorem dfom5

Description: _om is the smallest limit ordinal and can be defined as such (although the Axiom of Infinity is needed to ensure that at least one limit ordinal exists). (Contributed by FL, 22-Feb-2011) (Revised by Mario Carneiro, 2-Feb-2013)

Ref Expression
Assertion dfom5 ω = x | Lim x


Step Hyp Ref Expression
1 elom3 y ω x Lim x y x
2 vex y V
3 2 elintab y x | Lim x x Lim x y x
4 1 3 bitr4i y ω y x | Lim x
5 4 eqriv ω = x | Lim x