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Theorem homffn 14572
Description: The functionalized Hom-set operation is a function. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
homffn.f
homffn.b
Assertion
Ref Expression
homffn

Proof of Theorem homffn
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 homffn.f . . 3
2 homffn.b . . 3
3 eqid 2422 . . 3
41, 2, 3homffval 14570 . 2
5 ovex 6086 . 2
64, 5fnmpt2i 6612 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1687  X.cxp 4809  Fnwfn 5385  `cfv 5390  (class class class)co 6061   cbs 14114   chom 14189   chomf 14544
This theorem is referenced by:  homfeqbas  14575  2oppchomf  14603  subcss1  14692  issubc3  14699  fullsubc  14700  fullresc  14701  funcres2c  14751  hofcllem  15008  hofcl  15009  oppchofcl  15010  oyoncl  15020  yonffthlem  15032
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-8 1751  ax-9 1753  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403  ax-rep 4378  ax-sep 4388  ax-nul 4396  ax-pow 4442  ax-pr 4503  ax-un 6342
This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-3an 952  df-tru 1355  df-ex 1582  df-nf 1585  df-sb 1694  df-eu 2248  df-mo 2249  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-ral 2699  df-rex 2700  df-reu 2701  df-rab 2703  df-v 2953  df-sbc 3165  df-csb 3266  df-dif 3308  df-un 3310  df-in 3312  df-ss 3319  df-nul 3615  df-if 3769  df-pw 3839  df-sn 3859  df-pr 3860  df-op 3862  df-uni 4067  df-iun 4148  df-br 4268  df-opab 4326  df-mpt 4327  df-id 4607  df-xp 4817  df-rel 4818  df-cnv 4819  df-co 4820  df-dm 4821  df-rn 4822  df-res 4823  df-ima 4824  df-iota 5353  df-fun 5392  df-fn 5393  df-f 5394  df-f1 5395  df-fo 5396  df-f1o 5397  df-fv 5398  df-ov 6064  df-oprab 6065  df-mpt2 6066  df-1st 6546  df-2nd 6547  df-homf 14548
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