exlimdh - brismu bridi

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Theorem exlimdh 425

Description: Deduction converting universal quantification to existential quantification. (Contributed by la korvo, 9-Jul-2025.)

**Hypotheses**
Ref	Expression
exlimdh.0	⊢ ganai broda gi ro da zo'u broda
exlimdh.1	⊢ ganai brodi gi ro da zo'u brodi
exlimdh.2	⊢ ganai broda gi ganai brode gi brodi

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

**Proof of Theorem exlimdh**
Step	Hyp	Ref	Expression
1		exlimdh.0	. . 3 ⊢ ganai broda gi ro da zo'u broda
2		exlimdh.2	. . 3 ⊢ ganai broda gi ganai brode gi brodi
3	1, 2	alrimih 238	. 2 ⊢ ganai broda gi ro da zo'u ganai brode gi brodi
4		exlimdh.1	. . 3 ⊢ ganai brodi gi ro da zo'u brodi
5	4	eqih 422	. 2 ⊢ go ro da zo'u ganai brode gi brodi gi ganai su'o da zo'u brode gi brodi
6	3, 5	sylib 105	1 ⊢ ganai broda gi ganai su'o da zo'u brode gi brodi

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ro brd 222 su'o bsd 414

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-gen1 224 ax-qi1 234 ax-eq 420

This theorem depends on definitions: df-go 83

This theorem is referenced by: exim 426