brismu bridi		< Previous   Next > Nearby theorems
Mirrors  >  Home  >   Home  >  Th. List  >  id

---

Theorem id 18

Description: The principle of identity. This is distantly related to, but not the same as, the identity relation df-du 215. In terms of category theory, this proves that identity arrows exist. (Contributed by la korvo, 27-Jul-2023.)

Assertion

Ref	Expression
id	⊢ ganai broda gi broda

---

Proof of Theorem id

Step	Hyp	Ref	Expression
1		ax-k 11	. 2 ⊢ ganai broda gi ganai brode gi broda
2		ax-k 11	. 2 ⊢ ganai broda gi ganai ganai brode gi broda gi broda
3	1, 2	mpd 17	1 ⊢ ganai broda gi broda

Colors of variables: sumti selbri bridi

Syntax hints:  ganai bgan 9

This theorem was proved from axioms:  ax-mp 10  ax-k 11  ax-s 15

This theorem is referenced by:  idd  19  ganai-swap12  28  mpc  29  ganai-abs  32  imim2  37  mpancom  57  go-id  73  na.a-refl  92  ga-lin  142  ga-rin  143  ga-idem  145  na-gaiho  244  con2i  255  nakunaku  256  wit  386  nibli-refl  456  kihirnihi-refl  608

Copyright terms: Public domain

W3C validator