du-sym - brismu bridi

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Theorem du-sym 204

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

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

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

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

Step	Hyp	Ref	Expression
1		du-sym.0	. . . 4 ⊢ ko'a du ko'e
2	1	duis 199	. . 3 ⊢ go ko'a bu'a gi ko'e bu'a
3	2	go-comi 66	. 2 ⊢ go ko'e bu'a gi ko'a bu'a
4	3	duris 201	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 14 ax-ge-le 34 ax-ge-re 35 ax-ge-in 36 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: se-du-elim 205