syl5com - brismu bridi

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Theorem syl5com 25

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

**Hypotheses**
Ref	Expression
syl5com.0	⊢ ganai broda gi brode
syl5com.1	⊢ ganai brodi gi ganai brode gi brodo

**Assertion**
Ref	Expression
syl5com	⊢ ganai broda gi ganai brodi gi brodo

**Proof of Theorem syl5com**
Step	Hyp	Ref	Expression
1		syl5com.0	. . 3 ⊢ ganai broda gi brode
2	1	kd 24	. 2 ⊢ ganai broda gi ganai brodi gi brode
3		syl5com.1	. 2 ⊢ ganai brodi gi ganai brode gi brodo
4	2, 3	sylcom 21	1 ⊢ ganai broda gi ganai brodi gi brodo

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14

This theorem is referenced by: ganai-swap12 26 syl5 27