ge-pair - brismu bridi

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Theorem ge-pair 79

Description: A universal property of products: given two arrows in Loj, there is an arrow from the product of their sources to the product of their targets. (Contributed by la korvo, 9-Jul-2025.)

**Hypotheses**
Ref	Expression
ge-pair.0	⊢ ganai broda gi brode
ge-pair.1	⊢ ganai brodi gi brodo

**Assertion**
Ref	Expression
ge-pair	⊢ ganai ge broda gi brodi gi ge brode gi brodo

**Proof of Theorem ge-pair**
Step	Hyp	Ref	Expression
1		ge-pair.0	. 2 ⊢ ganai broda gi brode
2		ge-pair.1	. 2 ⊢ ganai brodi gi brodo
3		id 19	. 2 ⊢ ganai ge brode gi brodo gi ge brode gi brodo
4	1, 2, 3	syl2an 78	1 ⊢ ganai ge broda gi brodi gi ge brode gi brodo

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

This theorem is referenced by: ge-pairl 80 ge-pairr 81

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