exlimih - brismu bridi

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Theorem exlimih 424

Description: Convert universal quantification to existential quantification on top of an inference. (Contributed by la korvo, 9-Jul-2025.)

**Hypotheses**
Ref	Expression
exlimih.0	⊢ ganai brode gi ro da zo'u brode
exlimih.1	⊢ ganai broda gi brode

**Assertion**
Ref	Expression
exlimih	⊢ ganai su'o da zo'u broda gi brode

**Proof of Theorem exlimih**
Step	Hyp	Ref	Expression
1		exlimih.0	. . 3 ⊢ ganai brode gi ro da zo'u brode
2	1	eqih 422	. 2 ⊢ go ro da zo'u ganai broda gi brode gi ganai su'o da zo'u broda gi brode
3		exlimih.1	. 2 ⊢ ganai broda gi brode
4	2, 3	big1 226	1 ⊢ ganai su'o da zo'u broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 su'o bsd 414

This theorem was proved from axioms: ax-mp 10 ax-ge-le 48 ax-gen1 224 ax-eq 420

This theorem depends on definitions: df-go 83

This theorem is referenced by: foml19.41 432