Theorem om0x

Description: Ordinal multiplication with zero. Definition 8.15 of TakeutiZaring p. 62. Unlike om0 , this version works whether or not A is an ordinal. However, since it is an artifact of our particular function value definition outside the domain, we will not use it in order to be conventional and present it only as a curiosity. (Contributed by NM, 1-Feb-1996) (New usage is discouraged.)

	Ref	Expression
Assertion	om0x	|- ( A .o (/) ) = (/)

Proof

Step	Hyp	Ref	Expression
1		om0	|- ( A e. On -> ( A .o (/) ) = (/) )
2	1	adantr	|- ( ( A e. On /\ (/) e. On ) -> ( A .o (/) ) = (/) )
3		fnom	|- .o Fn ( On X. On )
4	3	fndmi	|- dom .o = ( On X. On )
5	4	ndmov	|- ( -. ( A e. On /\ (/) e. On ) -> ( A .o (/) ) = (/) )
6	2 5	pm2.61i	|- ( A .o (/) ) = (/)