sylib - brismu bridi

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Theorem sylib 105

Description: Syllogism with a biconditional. (Contributed by la korvo, 25-Jun-2024.)

**Hypotheses**
Ref	Expression
sylib.0	⊢ ganai broda gi brode
sylib.1	⊢ go brode gi brodi

**Assertion**
Ref	Expression
sylib	⊢ ganai broda gi brodi

**Proof of Theorem sylib**
Step	Hyp	Ref	Expression
1		sylib.0	. 2 ⊢ ganai broda gi brode
2		sylib.1	. . 3 ⊢ go brode gi brodi
3	2	go-ganai 85	. 2 ⊢ ganai brode gi brodi
4	1, 3	syl 21	1 ⊢ ganai broda gi brodi

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

This theorem depends on definitions: df-go 83

This theorem is referenced by: exlimdh 427 subh 461