syl - brismu bridi

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Theorem syl 20

Description: The quintessential syllogism. This inference is a standard workhorse for producing deductive forms. In terms of category theory, it composes arrows. (Contributed by la korvo, 30-Jul-2023.)

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

**Assertion**
Ref	Expression
syl	⊢ ganai broda gi brodi

**Proof of Theorem syl**
Step	Hyp	Ref	Expression
1		syl.0	. 2 ⊢ ganai broda gi brode
2		syl.1	. . 3 ⊢ ganai brode gi brodi
3	2	ki 12	. 2 ⊢ ganai broda gi ganai brode gi brodi
4	1, 3	mpd 17	1 ⊢ ganai broda gi brodi

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 15

This theorem is referenced by: sd 21 sylcom 23 kd 26 syl2im 31 ge-led 47 ge-red 49 go-ganaid 69 sylbi 82 sylib 83 sylibr 84 ga-lid 150 ga-rid 151 se-dual 186 se-dual-l 187 se-dual-r 188 se-ganaii 189 se-ganair 190 spec1d 198 ro1-coms 213 sdod 247 efqd 250 stewart 259 gripau-trans 302 te-dual 364 te-dual-l 365 te-dual-r 366 te-ganaii 367 te-ganair 368 mapti-ckini 634

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