sumji-no - brismu bridi

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Theorem sumji-no 543

Description: Every natural number is equal to zero plus itself. (Contributed by la korvo, 30-Aug-2024.)

**Assertion**
Ref	Expression
sumji-no	⊢ li ku'i'a sumji li 0 li ku'i'a

**Proof of Theorem sumji-no**
Step	Hyp	Ref	Expression
1		ax-plus-zero 538	. 2 ⊢ li + ku'i'a 0 du li ku'i'a
2		df-sumji 542	. 2 ⊢ go li ku'i'a sumji li 0 li ku'i'a gi li + ku'i'a 0 du li ku'i'a
3	1, 2	bi-rev 80	1 ⊢ li ku'i'a sumji li 0 li ku'i'a

Colors of variables: sumti selbri bridi

Syntax hints: du sbdu 214 li sli 511 0 p0 512 + msuhi 537 sumji bsumji 541

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-plus-zero 538

This theorem depends on definitions: df-go 61 df-sumji 542

This theorem is referenced by: (None)