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Theorem ab2rexex2 6766
 Description: Existence of an existentially restricted class abstraction. normally has free-variable parameters , , and . Compare abrexex2 6755. (Contributed by NM, 20-Sep-2011.)
Hypotheses
Ref Expression
ab2rexex2.1
ab2rexex2.2
ab2rexex2.3
Assertion
Ref Expression
ab2rexex2
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,)   ()   ()

Proof of Theorem ab2rexex2
StepHypRef Expression
1 ab2rexex2.1 . 2
2 ab2rexex2.2 . . 3
3 ab2rexex2.3 . . 3
42, 3abrexex2 6755 . 2
51, 4abrexex2 6755 1
 Colors of variables: wff setvar class Syntax hints:   wcel 1762  cab 2445  wrex 2808  cvv 3106 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-8 1764  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-rep 4551  ax-sep 4561  ax-nul 4569  ax-pr 4679  ax-un 6567 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2272  df-mo 2273  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3108  df-sbc 3325  df-csb 3429  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-if 3933  df-sn 4021  df-pr 4023  df-op 4027  df-uni 4239  df-iun 4320  df-br 4441  df-opab 4499  df-mpt 4500  df-id 4788  df-xp 4998  df-rel 4999  df-cnv 5000  df-co 5001  df-dm 5002  df-rn 5003  df-res 5004  df-ima 5005  df-iota 5542  df-fun 5581  df-fn 5582  df-f 5583  df-f1 5584  df-fo 5585  df-f1o 5586  df-fv 5587 This theorem is referenced by:  brdom7disj  8898  brdom6disj  8899  lineset  34409
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