gar - brismu bridi

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Theorem gar 140

Description: Reverse implication of df-ga 138 (Contributed by la korvo, 31-Jul-2023.)

**Assertion**
Ref	Expression
gar	⊢ ganai ge ganai brode gi broda gi ganai brodi gi broda gi ganai ga brode gi brodi gi broda

**Proof of Theorem gar**
Step	Hyp	Ref	Expression
1		df-ga 138	. 2 ⊢ go ganai ga brode gi brodi gi broda gi ge ganai brode gi broda gi ganai brodi gi broda
2	1	bi-rev-syl 81	1 ⊢ ganai ge ganai brode gi broda gi ganai brodi gi broda gi ganai ga brode gi brodi 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 ax-ge-in 45

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

This theorem is referenced by: garii 144