sylc - brismu bridi

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Theorem sylc 35

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

**Hypotheses**
Ref	Expression
sylc.0	⊢ ganai broda gi brode
sylc.1	⊢ ganai broda gi brodi
sylc.2	⊢ ganai brode gi ganai brodi gi brodo

**Assertion**
Ref	Expression
sylc	⊢ ganai broda gi brodo

**Proof of Theorem sylc**
Step	Hyp	Ref	Expression
1		sylc.0	. . 3 ⊢ ganai broda gi brode
2		sylc.1	. . 3 ⊢ ganai broda gi brodi
3		sylc.2	. . 3 ⊢ ganai brode gi ganai brodi gi brodo
4	1, 2, 3	syl2im 33	. 2 ⊢ ganai broda gi ganai broda gi brodo
5	4	ganai-abs 34	1 ⊢ ganai broda gi brodo

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15

This theorem is referenced by: cur 59 ge-prod 69 syl2anc 70