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Theorem id 17

Description: The principle of identity. This is distantly related to, but not the same as, the identity relation df-du 197. 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

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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 16	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 14

This theorem is referenced by:  ganai-swap12  26  ganai-abs  29  mpancom  48  go-id  63  na.a-refl  82  ga-lin  132  ga-rin  133  ga-idem  135  na-gaiho  218  wit  348  nibli-refl  414  kihirnihi-refl  566

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