syl5 - brismu bridi

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Theorem syl5 27

Description: A syllogism which shuffles antecedents. (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
syl5.0	⊢ ganai broda gi brode
syl5.1	⊢ ganai brodi gi ganai brode gi brodo

**Assertion**
Ref	Expression
syl5	⊢ ganai brodi gi ganai broda gi brodo

**Proof of Theorem syl5**
Step	Hyp	Ref	Expression
1		syl5.0	. . 3 ⊢ ganai broda gi brode
2		syl5.1	. . 3 ⊢ ganai brodi gi ganai brode gi brodo
3	1, 2	syl5com 25	. 2 ⊢ ganai broda gi ganai brodi gi brodo
4	3	ganai-swap12 26	1 ⊢ ganai brodi gi ganai broda 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: syl2im 28 syl5bi 76