refl-kinra - brismu bridi

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Theorem refl-kinra 542

Description: If a selbri is reflexive over any metasyntactic terbri, then it is reflexive over any domain. (Contributed by la korvo, 13-Aug-2024.)

**Hypothesis**
Ref	Expression
refl-kinra.0	⊢ da bu'a da

**Assertion**
Ref	Expression
refl-kinra	⊢ pa ka ce'u bu'a ce'u kei kinra ko'e

**Proof of Theorem refl-kinra**
Step	Hyp	Ref	Expression
1		refl-kinra.0	. . . 4 ⊢ da bu'a da
2	1	ckiniri 351	. . 3 ⊢ da ckini da pa ka ce'u bu'a ce'u kei
3	2	poi-gen 468	. 2 ⊢ ro da poi ke'a cmima ko'e ku'o zo'u da ckini da pa ka ce'u bu'a ce'u kei
4	3	kinrari 541	1 ⊢ pa ka ce'u bu'a ce'u kei kinra ko'e

Colors of variables: sumti selbri bridi

Syntax hints: tsb 1 tss 2 cmima sbcmima 319 ce'u sc 340 pa spk 341

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-gen1 224

This theorem depends on definitions: df-go 83 df-ckini 349 df-poi-ro 465 df-kinra 540

This theorem is referenced by: du-kinra 543 gripau-kinra 544 pagbu-kinra 631 kihirnihi-kinra 680

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