pilji-no - brismu bridi

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Theorem pilji-no 618

Description: Every natural number times zero is zero. (Contributed by la korvo, 30-Aug-2024.)

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

**Proof of Theorem pilji-no**
Step	Hyp	Ref	Expression
1		ax-mul-zero 614	. . 3 ⊢ li pi'i ku'i'a no du li no
2	1	du-symi 259	. 2 ⊢ li no du li pi'i ku'i'a no
3		df-pilji 617	. 2 ⊢ go li no pilji li ku'i'a li no gi li no du li pi'i ku'i'a no
4	2, 3	bi-rev 102	1 ⊢ li no pilji li ku'i'a li no

Colors of variables: sumti selbri bridi

Syntax hints: du sbdu 250 li sli 579 no p0 580 pi'i mpihi 613 pilji bpilji 616

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-spec2 232 ax-qi2 239 ax-mul-zero 614

This theorem depends on definitions: df-go 83 df-o 198 df-du 251 df-pilji 617

This theorem is referenced by: (None)