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Theorem relfth 14111
Description: The set of faithful functors is a relation. (Contributed by Mario Carneiro, 26-Jan-2017.)
Assertion
Ref Expression
relfth  |-  Rel  ( C Faith  D )

Proof of Theorem relfth
StepHypRef Expression
1 fthfunc 14109 . 2  |-  ( C Faith 
D )  C_  ( C  Func  D )
2 relfunc 14064 . 2  |-  Rel  ( C  Func  D )
3 relss 4966 . 2  |-  ( ( C Faith  D )  C_  ( C  Func  D )  ->  ( Rel  ( C  Func  D )  ->  Rel  ( C Faith  D ) ) )
41, 2, 3mp2 9 1  |-  Rel  ( C Faith  D )
Colors of variables: wff set class
Syntax hints:    C_ wss 3322   Rel wrel 4886  (class class class)co 6084    Func cfunc 14056   Faith cfth 14105
This theorem is referenced by:  fthpropd  14123  fthres2  14134  cofth  14137
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-iun 4097  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fv 5465  df-ov 6087  df-oprab 6088  df-mpt2 6089  df-1st 6352  df-2nd 6353  df-func 14060  df-fth 14107
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