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Theorem relfth 15765
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 15763 . 2  |-  ( C Faith 
D )  C_  ( C  Func  D )
2 relfunc 15718 . 2  |-  Rel  ( C  Func  D )
3 relss 4942 . 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 setvar class
Syntax hints:    C_ wss 3442   Rel wrel 4859  (class class class)co 6305    Func cfunc 15710   Faith cfth 15759
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-8 1872  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pow 4603  ax-pr 4661  ax-un 6597
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-sbc 3306  df-csb 3402  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-iun 4304  df-br 4427  df-opab 4485  df-mpt 4486  df-id 4769  df-xp 4860  df-rel 4861  df-cnv 4862  df-co 4863  df-dm 4864  df-rn 4865  df-res 4866  df-ima 4867  df-iota 5565  df-fun 5603  df-fv 5609  df-ov 6308  df-oprab 6309  df-mpt2 6310  df-1st 6807  df-2nd 6808  df-func 15714  df-fth 15761
This theorem is referenced by:  fthpropd  15777  fthres2  15788  cofth  15791
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