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Theorem mapex 7445
Description: The class of all functions mapping one set to another is a set. Remark after Definition 10.24 of [Kunen] p. 31. (Contributed by Raph Levien, 4-Dec-2003.)
Assertion
Ref Expression
mapex
Distinct variable groups:   ,   ,

Proof of Theorem mapex
StepHypRef Expression
1 fssxp 5748 . . . 4
21ss2abi 3571 . . 3
3 df-pw 4014 . . 3
42, 3sseqtr4i 3536 . 2
5 xpexg 6602 . . 3
6 pwexg 4636 . . 3
75, 6syl 16 . 2
8 ssexg 4598 . 2
94, 7, 8sylancr 663 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  e.wcel 1818  {cab 2442   cvv 3109  C_wss 3475  ~Pcpw 4012  X.cxp 5002  -->wf 5589
This theorem is referenced by:  fnmap  7446  mapvalg  7449  isghm  16267  wlks  24519  wlkres  24522  trls  24538  crcts  24622  cycls  24623  measbase  28168  measval  28169  ismeas  28170  isrnmeas  28171  cnfex  31403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-pw 4014  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015  df-fun 5595  df-fn 5596  df-f 5597
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