ge-dist-ex - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > ge-dist-ex

Theorem ge-dist-ex 431

Description: Distribute existential quantification over conjunction. Theorem 19.40 of [Margaris] p. 90. (Contributed by la korvo, 9-Jul-2025.)

**Assertion**
Ref	Expression
ge-dist-ex	⊢ ganai su'o da zo'u ge broda gi brode gi ge su'o da zo'u broda gi su'o da zo'u brode

**Proof of Theorem ge-dist-ex**
Step	Hyp	Ref	Expression
1		ge-lex 430	. 2 ⊢ ganai su'o da zo'u ge broda gi brode gi su'o da zo'u broda
2		ax-ge-re 49	. . 3 ⊢ ganai ge broda gi brode gi brode
3	2	eximi 427	. 2 ⊢ ganai su'o da zo'u ge broda gi brode gi su'o da zo'u brode
4	1, 3	ge-prod 69	1 ⊢ ganai su'o da zo'u ge broda gi brode gi ge su'o da zo'u broda gi su'o da zo'u brode

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 47 su'o bsd 414

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-gen1 224 ax-spec1 228 ax-qi1 234 ax-ro1-nf 249 ax-eb 418 ax-eq 420

This theorem depends on definitions: df-go 83

This theorem is referenced by: foml19.41 432