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Theorem abrexexg 5780
 Description: Existence of a class abstraction of existentially restricted sets. is normally a free-variable parameter in . The antecedent assures us that is a set. (Contributed by NM, 3-Nov-2003.)
Assertion
Ref Expression
abrexexg
Distinct variable groups:   ,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem abrexexg
StepHypRef Expression
1 eqid 2296 . . 3
21rnmpt 4941 . 2
3 mptexg 5761 . . 3
4 rnexg 4956 . . 3
53, 4syl 15 . 2
62, 5syl5eqelr 2381 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1632   wcel 1696  cab 2282  wrex 2557  cvv 2801   cmpt 4093   crn 4706 This theorem is referenced by:  iunexg  5783  qsexg  6733  wdomd  7311  cardiun  7631  rankcf  8415  sigaclci  23508  ab2rexexg2  25224  intopcoaconlem3b  25641  intopcoaconlem3  25642  intopcoaconb  25643  hbtlem1  27430  hbtlem7  27432 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-rep 4147  ax-sep 4157  ax-nul 4165  ax-pr 4230  ax-un 4528 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-sbc 3005  df-csb 3095  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-iun 3923  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fn 5274  df-f 5275  df-f1 5276  df-fo 5277  df-f1o 5278  df-fv 5279
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