ga-rin - brismu bridi

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Theorem ga-rin 143

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 18	. . 3 ⊢ ganai ga brode gi broda gi ga brode gi broda
2		df-ga 138	. . 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 79	. 2 ⊢ ge ganai brode gi ga brode gi broda gi ganai broda gi ga brode gi broda
4	3	ge-rei 48	1 ⊢ ganai broda gi ga brode gi broda

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ge bge 42 ga bga 137

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 43 ax-ge-re 44

This theorem depends on definitions: df-go 61 df-ga 138

This theorem is referenced by: ga-com-lem 146 ga-ri 149 ga-rid 151 ceri-rin 374 cmima-zilcmi 411