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Theorem relfull 13831
Description: The set of full functors is a relation. (Contributed by Mario Carneiro, 26-Jan-2017.)
Assertion
Ref Expression
relfull  |-  Rel  ( C Full  D )

Proof of Theorem relfull
StepHypRef Expression
1 fullfunc 13829 . 2  |-  ( C Full 
D )  C_  ( C  Func  D )
2 relfunc 13785 . 2  |-  Rel  ( C  Func  D )
3 relss 4812 . 2  |-  ( ( C Full  D )  C_  ( C  Func  D )  ->  ( Rel  ( C  Func  D )  ->  Rel  ( C Full  D ) ) )
41, 2, 3mp2 17 1  |-  Rel  ( C Full  D )
Colors of variables: wff set class
Syntax hints:    C_ wss 3186   Rel wrel 4731  (class class class)co 5900    Func cfunc 13777   Full cful 13825
This theorem is referenced by:  fullpropd  13843  cofull  13857
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-13 1703  ax-14 1705  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-nul 4186  ax-pow 4225  ax-pr 4251  ax-un 4549
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-eu 2180  df-mo 2181  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-ral 2582  df-rex 2583  df-rab 2586  df-v 2824  df-sbc 3026  df-csb 3116  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-sn 3680  df-pr 3681  df-op 3683  df-uni 3865  df-iun 3944  df-br 4061  df-opab 4115  df-mpt 4116  df-id 4346  df-xp 4732  df-rel 4733  df-cnv 4734  df-co 4735  df-dm 4736  df-rn 4737  df-res 4738  df-ima 4739  df-iota 5256  df-fun 5294  df-fn 5295  df-f 5296  df-fv 5300  df-ov 5903  df-oprab 5904  df-mpt2 5905  df-1st 6164  df-2nd 6165  df-func 13781  df-full 13827
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