ga-rin - brismu bridi

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Theorem ga-rin 166

Description: Introduce {ga} with the antecedent on the right. (Contributed by la korvo, 31-Jul-2023.)

**Assertion**
Ref	Expression
ga-rin	⊢ ganai broda gi ga brode gi broda

**Proof of Theorem ga-rin**
Step	Hyp	Ref	Expression
1		id 19	. . 3 ⊢ ganai ga brode gi broda gi ga brode gi broda
2		df-ga 161	. . 3 ⊢ go ganai ga brode gi broda gi ga brode gi broda gi ge ganai brode gi ga brode gi broda gi ganai broda gi ga brode gi broda
3	1, 2	bi 101	. 2 ⊢ ge ganai brode gi ga brode gi broda gi ganai broda gi ga brode gi broda
4	3	ge-rei 53	1 ⊢ ganai broda gi ga brode gi broda

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ge bge 47 ga bga 160

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49

This theorem depends on definitions: df-go 83 df-ga 161

This theorem is referenced by: ga-com-lem 172 ge-dist-ga 174 ga-ri 176 ga-rid 178 ga-dist-ge 182 ceri-rin 411 cmima-zilcmi 462