lnci - brismu bridi

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Theorem lnci 240

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 120	. . 3 ⊢ go ge broda gi naku broda gi ge naku broda gi broda
3	1, 2	bi 79	. 2 ⊢ ge naku broda gi broda
4		naku-uncur 238	. 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 42 gai'o bgaiho 235 naku bnk 236

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

This theorem depends on definitions: df-go 61 df-naku 237

This theorem is referenced by: (None)

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