sylanbrc - brismu bridi

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Theorem sylanbrc 75

Description: Deductive unpacking of a definition with conjoined components. Theorem sylanbrc in [ILE] p. 0. (Contributed by la korvo, 22-Jun-2024.)

**Hypotheses**
Ref	Expression
sylanbrc.0	⊢ ganai broda gi brode
sylanbrc.1	⊢ ganai broda gi brodi
sylanbrc.2	⊢ go brodo gi ge brode gi brodi

**Assertion**
Ref	Expression
sylanbrc	⊢ ganai broda gi brodo

**Proof of Theorem sylanbrc**
Step	Hyp	Ref	Expression
1		sylanbrc.0	. . 3 ⊢ ganai broda gi brode
2		sylanbrc.1	. . 3 ⊢ ganai broda gi brodi
3	1, 2	jca 46	. 2 ⊢ ganai broda gi ge brode gi brodi
4		sylanbrc.2	. 2 ⊢ go brodo gi ge brode gi brodi
5	3, 4	sylibr 74	1 ⊢ ganai broda gi brodo

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 33

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14 ax-ge-le 34 ax-ge-re 35 ax-ge-in 36

This theorem depends on definitions: df-go 52

This theorem is referenced by: subeq-lem1 353

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