syl6 - brismu bridi

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Theorem syl6 25

Description: A syllogism replacing consequents. (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
syl6.0	⊢ ganai broda gi ganai brode gi brodi
syl6.1	⊢ ganai brodi gi brodo

**Assertion**
Ref	Expression
syl6	⊢ ganai broda gi ganai brode gi brodo

**Proof of Theorem syl6**
Step	Hyp	Ref	Expression
1		syl6.0	. 2 ⊢ ganai broda gi ganai brode gi brodi
2		syl6.1	. . 3 ⊢ ganai brodi gi brodo
3	2	ki 12	. 2 ⊢ ganai brode gi ganai brodi gi brodo
4	1, 3	sylcom 24	1 ⊢ ganai broda gi ganai brode gi brodo

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: syl6c 26 uncur 61 con2d 289