syl9 - brismu bridi

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Theorem syl9 40

Description: A syllogism. (Contributed by la korvo, 1-Jan-2025.)

**Hypotheses**
Ref	Expression
syl9.1	⊢ ganai broda gi ganai brode gi brodi
syl9.2	⊢ ganai brodo gi ganai brodi gi brodu

**Assertion**
Ref	Expression
syl9	⊢ ganai broda gi ganai brodo gi ganai brode gi brodu

**Proof of Theorem syl9**
Step	Hyp	Ref	Expression
1		syl9.1	. 2 ⊢ ganai broda gi ganai brode gi brodi
2		syl9.2	. . 3 ⊢ ganai brodo gi ganai brodi gi brodu
3	2	ki 12	. 2 ⊢ ganai broda gi ganai brodo gi ganai brodi gi brodu
4	1, 3	syl5d 39	1 ⊢ ganai broda gi ganai brodo gi ganai brode gi brodu

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

This theorem is referenced by: ganai-swap23 41