ge-lex - brismu bridi

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Theorem ge-lex 430

Description: Universal property of products ax-ge-le 48 underneath existential quantification. (Contributed by la korvo, 9-Jul-2025.)

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

**Proof of Theorem ge-lex**
Step	Hyp	Ref	Expression
1		ax-ge-le 48	. 2 ⊢ ganai ge broda gi brode gi broda
2	1	eximi 427	1 ⊢ ganai su'o da zo'u ge broda gi brode gi su'o da zo'u broda

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 47

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: ge-dist-ex 431