sylanbrc - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > sylanbrc

Theorem sylanbrc 107

Description: Deductive unpacking of a definition with conjoined components. (Contributed by la korvo, 22-Jun-2024.)

**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	ge-prod 69	. 2 ⊢ ganai broda gi ge brode gi brodi
4		sylanbrc.2	. 2 ⊢ go brodo gi ge brode gi brodi
5	3, 4	sylibr 106	1 ⊢ ganai broda 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-re 49 ax-ge-in 50

This theorem depends on definitions: df-go 83

This theorem is referenced by: subeq-lem1 452 sub2 456