syldan - brismu bridi

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Theorem syldan 66

Description: A syllogism flattening a nested pair. (Contributed by la korvo, 9-Jul-2025.)

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

**Assertion**
Ref	Expression
syldan	⊢ ganai ge broda gi brode gi brodo

**Proof of Theorem syldan**
Step	Hyp	Ref	Expression
1		syldan.0	. 2 ⊢ ganai ge broda gi brode gi brodi
2		syldan.1	. . . 4 ⊢ ganai ge broda gi brodi gi brodo
3	2	uncur-swap12 62	. . 3 ⊢ ganai brodi gi ganai broda gi brodo
4	3	weakard 64	. 2 ⊢ ganai brodi gi ganai ge broda gi brode gi brodo
5	1, 4	mpcom 30	1 ⊢ ganai ge broda gi 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-in 50

This theorem is referenced by: sylan2 68