du-trans - brismu bridi

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Theorem du-trans 203

Description: {du} is transitive. (Contributed by la korvo, 16-Aug-2023.) (Shortened by la korvo, 23-Jun-2024.)

**Hypotheses**
Ref	Expression
du-trans.0	⊢ ko'a du ko'e
du-trans.1	⊢ ko'e du ko'i

**Assertion**
Ref	Expression
du-trans	⊢ ko'a du ko'i

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

Step	Hyp	Ref	Expression
1		du-trans.0	. . . 4 ⊢ ko'a du ko'e
2	1	duis 199	. . 3 ⊢ go ko'a bu'a gi ko'e bu'a
3		du-trans.1	. . . 4 ⊢ ko'e du ko'i
4	3	duis 199	. . 3 ⊢ go ko'e bu'a gi ko'i bu'a
5	2, 4	go-syl 68	. 2 ⊢ go ko'a bu'a gi ko'i bu'a
6	5	duris 201	1 ⊢ ko'a du ko'i

Colors of variables: sumti selbri bridi

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-go-trans 67 ax-gen2 180 ax-spec2 183 ax-qi2 188

This theorem depends on definitions: df-go 52 df-o 153 df-du 197

This theorem is referenced by: (None)