garian - brismu bridi

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Theorem garian 170

Description: Disjunction over conjunctions in the antecedents. (Contributed by la korvo, 14-Jul-2025.)

**Hypotheses**
Ref	Expression
garian.0	⊢ ganai ge broda gi brode gi brodi
garian.1	⊢ ganai ge brodo gi brode gi brodi

**Assertion**
Ref	Expression
garian	⊢ ganai ge ga broda gi brodo gi brode gi brodi

**Proof of Theorem garian**
Step	Hyp	Ref	Expression
1		garian.0	. . . 4 ⊢ ganai ge broda gi brode gi brodi
2	1	uncur 61	. . 3 ⊢ ganai broda gi ganai brode gi brodi
3		garian.1	. . . 4 ⊢ ganai ge brodo gi brode gi brodi
4	3	uncur 61	. . 3 ⊢ ganai brodo gi ganai brode gi brodi
5	2, 4	ga-sum 167	. 2 ⊢ ganai ga broda gi brodo gi ganai brode gi brodi
6	5	cur 59	1 ⊢ ganai ge ga broda gi brodo gi brode gi brodi

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ga bga 160

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49 ax-ge-in 50

This theorem depends on definitions: df-go 83 df-ga 161

This theorem is referenced by: ga-dist-ge 182