zilcmi-nomei - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > zilcmi-nomei

Theorem zilcmi-nomei 461

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 256	. . 3 ⊢ le nomei ku du le nomei ku
2		ga-lin 165	. . 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 460	. 2 ⊢ go le nomei ku zilcmi gi ga le nomei ku du le nomei ku gi su'o da zo'u da cmima le nomei ku
5	3, 4	bi-rev 102	1 ⊢ le nomei ku zilcmi

Colors of variables: sumti selbri bridi

Syntax hints: ga bga 160 du sbdu 250 cmima sbcmima 319 le snomei 323 su'o bsd 414 zilcmi sbzilcmi 459

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49 ax-ge-in 50 ax-gen2 227 ax-qi2 239

This theorem depends on definitions: df-go 83 df-ga 161 df-o 198 df-du 251 df-zilcmi 460

This theorem is referenced by: (None)