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Theorem gonaii 299

Description: Inference form of df-gonai 298 (Contributed by la korvo, 8-Aug-2023.)

**Hypothesis**
Ref	Expression
gonaii.0	⊢ gonai broda gi brode

**Assertion**
Ref	Expression
gonaii	⊢ ge ga broda gi brode gi naku ge broda gi brode

**Proof of Theorem gonaii**
Step	Hyp	Ref	Expression
1		gonaii.0	. 2 ⊢ gonai broda gi brode
2		df-gonai 298	. 2 ⊢ go gonai broda gi brode gi ge ga broda gi brode gi naku ge broda gi brode
3	1, 2	bi 101	1 ⊢ ge ga broda gi brode gi naku ge broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 47 ga bga 160 naku bnk 272 gonai bgon 297

This theorem was proved from axioms: ax-mp 10 ax-ge-le 48

This theorem depends on definitions: df-go 83 df-gonai 298

This theorem is referenced by: gonaiil 300 gonaiir 301