gonaiir - brismu bridi

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Theorem gonaiir 264

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

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

**Assertion**
Ref	Expression
gonaiir	⊢ naku ge broda gi brode

**Proof of Theorem gonaiir**
Step	Hyp	Ref	Expression
1		gonaiir.0	. . 3 ⊢ gonai broda gi brode
2	1	gonaii 262	. 2 ⊢ ge ga broda gi brode gi naku ge broda gi brode
3	2	ge-rei 48	1 ⊢ naku ge broda gi brode

Colors of variables: sumti selbri bridi

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

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

This theorem depends on definitions: df-go 61 df-gonai 261

This theorem is referenced by: (None)