pilji-no - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > pilji-no

Theorem pilji-no 508

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

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

**Proof of Theorem pilji-no**
Step	Hyp	Ref	Expression
1		ax-mul-zero 504	. 2 ⊢ li * ku'i'a 0 du li 0
2		df-pilji 507	. 2 ⊢ go li ku'i'a pilji li 0 li 0 gi li * ku'i'a 0 du li 0
3	1, 2	bi-rev 70	1 ⊢ li ku'i'a pilji li 0 li 0

Colors of variables: sumti selbri bridi

Syntax hints: du sbdu 196 li sli 469 0 p0 470 * mpihi 503 pilji bpilji 506

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14 ax-ge-le 34 ax-ge-re 35 ax-ge-in 36 ax-mul-zero 504

This theorem depends on definitions: df-go 52 df-pilji 507

This theorem is referenced by: (None)