lnci - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > lnci

Theorem lnci 276

Description: The law of non-contradiction. If a bridi is simultaneously inhabited and uninhabited, then we reach an absurdity. (Contributed by la korvo, 20-Aug-2023.)

**Hypothesis**
Ref	Expression
lnci.0	⊢ ge broda gi naku broda

**Assertion**
Ref	Expression
lnci	⊢ gai'o

**Proof of Theorem lnci**
Step	Hyp	Ref	Expression
1		lnci.0	. . 3 ⊢ ge broda gi naku broda
2		ge-com 142	. . 3 ⊢ go ge broda gi naku broda gi ge naku broda gi broda
3	1, 2	bi 101	. 2 ⊢ ge naku broda gi broda
4		naku-uncur 274	. 2 ⊢ ganai ge naku broda gi broda gi gai'o
5	3, 4	ax-mp 10	1 ⊢ gai'o

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 47 gai'o bgaiho 271 naku bnk 272

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

This theorem depends on definitions: df-go 83 df-naku 273

This theorem is referenced by: (None)

W3C validator