gonairi - brismu bridi

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Theorem gonairi 265

Description: Reverse inference form of df-gonai 261 (Contributed by la korvo, 8-Aug-2023.)

**Hypothesis**
Ref	Expression
gonairi.0	⊢ ge ga broda gi brode gi naku ge broda gi brode

**Assertion**
Ref	Expression
gonairi	⊢ gonai broda gi brode

**Proof of Theorem gonairi**
Step	Hyp	Ref	Expression
1		gonairi.0	. 2 ⊢ ge ga broda gi brode gi naku ge broda gi brode
2		df-gonai 261	. 2 ⊢ go gonai broda gi brode gi ge ga broda gi brode gi naku ge broda gi brode
3	1, 2	bi-rev 80	1 ⊢ gonai broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 42 ga bga 137 naku bnk 236 gonai bgon 260

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-gonai 261

This theorem is referenced by: (None)