syl2an - brismu bridi

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Theorem syl2an 78

Description: A double syllogism. (Contributed by la korvo, 9-Jul-2025.)

**Hypotheses**
Ref	Expression
syl2an.0	⊢ ganai broda gi brode
syl2an.1	⊢ ganai brodu gi brodi
syl2an.2	⊢ ganai ge brode gi brodi gi brodo

**Assertion**
Ref	Expression
syl2an	⊢ ganai ge broda gi brodu gi brodo

**Proof of Theorem syl2an**
Step	Hyp	Ref	Expression
1		syl2an.1	. 2 ⊢ ganai brodu gi brodi
2		syl2an.0	. . 3 ⊢ ganai broda gi brode
3		syl2an.2	. . 3 ⊢ ganai ge brode gi brodi gi brodo
4	2, 3	sylan 77	. 2 ⊢ ganai ge broda gi brodi gi brodo
5	1, 4	sylan2 68	1 ⊢ ganai ge broda gi brodu gi brodo

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49 ax-ge-in 50

This theorem is referenced by: ge-pair 79