sylan - brismu bridi

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Theorem sylan 77

Description: A syllogism refining a conjunction. (Contributed by la korvo, 9-Jul-2025.)

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

**Assertion**
Ref	Expression
sylan	⊢ ganai ge broda gi brodi gi brodo

**Proof of Theorem sylan**
Step	Hyp	Ref	Expression
1		sylan.0	. 2 ⊢ ganai broda gi brode
2		sylan.1	. . 3 ⊢ ganai ge brode gi brodi gi brodo
3	2	uncur-swap12 62	. 2 ⊢ ganai brodi gi ganai brode gi brodo
4	1, 3	mpan9 76	1 ⊢ ganai ge broda gi brodi gi brodo

Colors of variables: sumti selbri bridi

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: syl2an 78