du-symi - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > du-symi

Theorem du-symi 259

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 253	. . 3 ⊢ go ko'a bu'a gi ko'e bu'a
3	2	go-comi 98	. 2 ⊢ go ko'e bu'a gi ko'a bu'a
4	3	duris 255	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 48 ax-ge-re 49 ax-ge-in 50 ax-gen2 227 ax-spec2 232 ax-qi2 239

This theorem depends on definitions: df-go 83 df-o 198 df-du 251

This theorem is referenced by: se-du-elim 262