garii - brismu bridi

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Theorem garii 144

Description: Nested inference form of gar 140 (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
garii.0	⊢ ganai broda gi brode
garii.1	⊢ ganai brodi gi brode

**Assertion**
Ref	Expression
garii	⊢ ganai ga broda gi brodi gi brode

**Proof of Theorem garii**
Step	Hyp	Ref	Expression
1		garii.0	. 2 ⊢ ganai broda gi brode
2		garii.1	. 2 ⊢ ganai brodi gi brode
3		gar 140	. 2 ⊢ ganai ge ganai broda gi brode gi ganai brodi gi brode gi ganai ga broda gi brodi gi brode
4	1, 2, 3	mp2an 59	1 ⊢ ganai ga broda gi brodi gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 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: ga-idem 145 ga-com-lem 146