ro1-coms - brismu bridi

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Theorem ro1-coms 213

Description: Swap quantifiers on the antecedent. (Contributed by la korvo, 4-Jan-2025.)

**Hypothesis**
Ref	Expression
ro1-coms.0	⊢ ganai ro da zo'u ro de zo'u broda gi brode

**Assertion**
Ref	Expression
ro1-coms	⊢ ganai ro de zo'u ro da zo'u broda gi brode

Distinct variable group: da ,de

**Proof of Theorem ro1-coms**
Step	Hyp	Ref	Expression
1		ax-ro1-com 212	. 2 ⊢ ganai ro de zo'u ro da zo'u broda gi ro da zo'u ro de zo'u broda
2		ro1-coms.0	. 2 ⊢ ganai ro da zo'u ro de zo'u broda gi brode
3	1, 2	syl 20	1 ⊢ ganai ro de zo'u ro da zo'u broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ro brd 191

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ro1-com 212

This theorem is referenced by: (None)