ga-lin - brismu bridi

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Theorem ga-lin 165

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

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

**Proof of Theorem ga-lin**
Step	Hyp	Ref	Expression
1		id 19	. . 3 ⊢ ganai ga broda gi brode gi ga broda gi brode
2		df-ga 161	. . 3 ⊢ go ganai ga broda gi brode gi ga broda gi brode gi ge ganai broda gi ga broda gi brode gi ganai brode gi ga broda gi brode
3	1, 2	bi 101	. 2 ⊢ ge ganai broda gi ga broda gi brode gi ganai brode gi ga broda gi brode
4	3	ge-lei 51	1 ⊢ ganai broda gi ga broda gi brode

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

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

This theorem is referenced by: ga-idem 171 ga-com-lem 172 ge-dist-ga 174 ga-li 175 ga-lid 177 ga-dist-ge 182 ceri-lin 410 zilcmi-nomei 461