sylbi - brismu bridi

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Theorem sylbi 72

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

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

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

**Proof of Theorem sylbi**
Step	Hyp	Ref	Expression
1		sylbi.0	. . 3 ⊢ go broda gi brode
2	1	go-ganai 54	. 2 ⊢ ganai broda gi brode
3		sylbi.1	. 2 ⊢ ganai brode gi brodi
4	2, 3	syl 18	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 14 ax-ge-le 34

This theorem depends on definitions: df-go 52

This theorem is referenced by: nfr 360