sylcom - brismu bridi

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Theorem sylcom 21

Description: A syllogism which shuffles antecedents. (Contributed by la korvo, 30-Jul-2023.)

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

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

**Proof of Theorem sylcom**
Step	Hyp	Ref	Expression
1		sylcom.0	. 2 ⊢ ganai broda gi ganai brode gi brodi
2		sylcom.1	. . 3 ⊢ ganai brode gi ganai brodi gi brodo
3	2	si 15	. 2 ⊢ ganai ganai brode gi brodi gi ganai brode gi brodo
4	1, 3	syl 18	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 14

This theorem is referenced by: syl6 22 syl5com 25