du-syms - brismu bridi

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Theorem du-syms 262

Description: Commute an equality in an antecedent. (Contributed by la korvo, 11-Aug-2026.)

**Hypothesis**
Ref	Expression
du-syms.0	⊢ ganai ko'a du ko'e gi broda

**Assertion**
Ref	Expression
du-syms	⊢ ganai ko'e du ko'a gi broda

**Proof of Theorem du-syms**
Step	Hyp	Ref	Expression
1		du-sym-ganai 260	. 2 ⊢ ganai ko'e du ko'a gi ko'a du ko'e
2		du-syms.0	. 2 ⊢ ganai ko'a du ko'e gi broda
3	1, 2	syl 21	1 ⊢ ganai ko'e du ko'a gi broda

Colors of variables: sumti selbri bridi

Syntax hints: du sbdu 250

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-qi2 239 ax-du-trans 258

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

This theorem is referenced by: stdpc7 460