du-symi - brismu bridi

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Theorem du-symi 223

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

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

**Assertion**
Ref	Expression
du-symi	⊢ ko'e du ko'a

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

Step	Hyp	Ref	Expression
1		du-symi.0	. . . 4 ⊢ ko'a du ko'e
2	1	duis 217	. . 3 ⊢ go ko'a bu'a gi ko'e bu'a
3	2	go-comi 76	. 2 ⊢ go ko'e bu'a gi ko'a bu'a
4	3	duris 219	1 ⊢ ko'e du ko'a

Colors of variables: sumti selbri bridi

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-gen2 195 ax-spec2 199 ax-qi2 204

This theorem depends on definitions: df-go 61 df-o 167 df-du 215

This theorem is referenced by: se-du-elim 226