du-dunli - brismu bridi

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Theorem du-dunli 372

Description: Suggested by CLL definition of {dunli}: {du} is {dunli} without a standard of comparison, which is a stronger condition. See discussion around example 7.2 from [CLL] p. 18. (Contributed by la korvo, 10-Aug-2026.)

**Hypothesis**
Ref	Expression
du-dunli.0	⊢ ko'a du ko'e

**Assertion**
Ref	Expression
du-dunli	⊢ ko'a dunli ko'e ko'i

Proof of Theorem du-dunli Dummy variable bu'a is distinct from all other variables.

Step	Hyp	Ref	Expression
1		tss 2	. . 3 brirebla ckini ko'o ko'i
2		du-dunli.0	. . . 4 ⊢ ko'a du ko'e
3	2	dui 252	. . 3 ⊢ ro bu'a zo'u ko'a .o ko'e bu'a
4	1, 3	ax-ro-inst-2u 242	. 2 ⊢ ko'a .o ko'e ckini ko'o ko'i
5	4	dunliri 369	1 ⊢ ko'a dunli ko'e ko'i

Colors of variables: sumti selbri bridi

Syntax hints: tsb 1 tss 2 .o sjo 197 ckini sbckini 348

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-ro-inst-2u 242

This theorem depends on definitions: df-go 83 df-du 251 df-dunli 367

This theorem is referenced by: (None)

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