pilji-no - brismu bridi

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

Theorem pilji-no 550

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 546	. 2 ⊢ li * ku'i'a 0 du li 0
2		df-pilji 549	. 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 80	1 ⊢ li ku'i'a pilji li 0 li 0

Colors of variables: sumti selbri bridi

Syntax hints: du sbdu 214 li sli 511 0 p0 512 * mpihi 545 pilji bpilji 548

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-mul-zero 546

This theorem depends on definitions: df-go 61 df-pilji 549

This theorem is referenced by: (None)