iso - brismu bridi

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Theorem iso 65

Description: Inference form of right side of gori 64 (Contributed by la korvo, 30-Jul-2023.)

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

**Assertion**
Ref	Expression
iso	⊢ go broda gi brode

**Proof of Theorem iso**
Step	Hyp	Ref	Expression
1		iso.0	. . 3 ⊢ ganai broda gi brode
2		iso.1	. . 3 ⊢ ganai brode gi broda
3	1, 2	ge-ini 50	. 2 ⊢ ge ganai broda gi brode gi ganai brode gi broda
4	3	gori 64	1 ⊢ go broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-re 44 ax-ge-in 45

This theorem depends on definitions: df-go 61

This theorem is referenced by: go-id 73 go-com 75 ge-com 120 ge-go 121 ge-idem 123 ga-idem 145 ga-com 147 du-sym-go 225