zilcmi-nomei - brismu bridi

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Theorem zilcmi-nomei 410

Description: The empty set is a set. (Contributed by la korvo, 19-Sep-2024.)

**Assertion**
Ref	Expression
zilcmi-nomei	⊢ le nomei ku zilcmi

Proof of Theorem zilcmi-nomei Dummy variable da is distinct from all other variables.

Step	Hyp	Ref	Expression
1		du-refl 220	. . 3 ⊢ le nomei ku du le nomei ku
2		ga-lin 142	. . 3 ⊢ ganai le nomei ku du le nomei ku gi ga le nomei ku du le nomei ku gi su'o da zo'u da cmima le nomei ku
3	1, 2	ax-mp 10	. 2 ⊢ ga le nomei ku du le nomei ku gi su'o da zo'u da cmima le nomei ku
4		df-zilcmi 409	. 2 ⊢ go le nomei ku zilcmigi ga le nomei ku du le nomei ku gi su'o da zo'u da cmima le nomei ku
5	3, 4	bi-rev 80	1 ⊢ le nomei ku zilcmi

Colors of variables: sumti selbri bridi

Syntax hints: ga bga 137 du sbdu 214 cmima sbcmima 282 le snomei 286 su'o bsd 377 zilcmisbzilcmi 408

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 43 ax-ge-re 44 ax-ge-in 45 ax-gen2 195 ax-qi2 204

This theorem depends on definitions: df-go 61 df-ga 138 df-o 167 df-du 215 df-zilcmi 409

This theorem is referenced by: (None)