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Theorem relfth 16340
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 16338 . 2 (𝐶 Faith 𝐷) ⊆ (𝐶 Func 𝐷)
2 relfunc 16293 . 2 Rel (𝐶 Func 𝐷)
3 relss 5118 . 2 ((𝐶 Faith 𝐷) ⊆ (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:  wss 3539  Rel wrel 5032  (class class class)co 6526   Func cfunc 16285   Faith cfth 16334
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-8 1978  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4711  ax-pow 4763  ax-pr 4827  ax-un 6824
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rex 2901  df-rab 2904  df-v 3174  df-sbc 3402  df-csb 3499  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-uni 4367  df-iun 4451  df-br 4578  df-opab 4638  df-mpt 4639  df-id 4942  df-xp 5033  df-rel 5034  df-cnv 5035  df-co 5036  df-dm 5037  df-rn 5038  df-res 5039  df-ima 5040  df-iota 5753  df-fun 5791  df-fv 5797  df-ov 6529  df-oprab 6530  df-mpt2 6531  df-1st 7036  df-2nd 7037  df-func 16289  df-fth 16336
This theorem is referenced by:  fthpropd  16352  fthres2  16363  cofth  16366
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