syl - brismu bridi

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Theorem syl 21

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 18	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 22 sylcom 24 kd 27 syl2im 33 ge-led 52 ge-red 54 go-ganaid 91 sylbi 104 sylib 105 sylibr 106 ga-lid 177 ga-rid 178 se-dual 217 se-dual-l 218 se-dual-r 219 se-ganaii 220 se-ganair 221 spec1d 230 spec1s 231 alrimih 238 ro1-coms 248 sdod 283 efqd 286 stewart 296 gripau-trans 339 te-dual 401 te-dual-l 402 te-dual-r 403 te-ganaii 404 te-ganair 405 eximdh 428 foml19.29 429 foml19.41 432 equs4 453 stdpc4 455 subh 456 mapti-ckini 709

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