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Theorem oprabrexex2 6802
 Description: Existence of an existentially restricted operation abstraction. (Contributed by Jeff Madsen, 11-Jun-2010.)
Hypotheses
Ref Expression
oprabrexex2.1
oprabrexex2.2
Assertion
Ref Expression
oprabrexex2
Distinct variable group:   ,,,,
Allowed substitution hints:   (,,,)

Proof of Theorem oprabrexex2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-oprab 6312 . . 3
2 rexcom4 3053 . . . . 5
3 rexcom4 3053 . . . . . . 7
4 rexcom4 3053 . . . . . . . . 9
5 r19.42v 2931 . . . . . . . . . 10
65exbii 1726 . . . . . . . . 9
74, 6bitri 257 . . . . . . . 8
87exbii 1726 . . . . . . 7
93, 8bitri 257 . . . . . 6
109exbii 1726 . . . . 5
112, 10bitr2i 258 . . . 4
1211abbii 2587 . . 3
131, 12eqtri 2493 . 2
14 oprabrexex2.1 . . 3
15 df-oprab 6312 . . . 4
16 oprabrexex2.2 . . . 4
1715, 16eqeltrri 2546 . . 3
1814, 17abrexex2 6793 . 2
1913, 18eqeltri 2545 1
 Colors of variables: wff setvar class Syntax hints:   wa 376   wceq 1452  wex 1671   wcel 1904  cab 2457  wrex 2757  cvv 3031  cop 3965  coprab 6309 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-rep 4508  ax-sep 4518  ax-nul 4527  ax-pr 4639  ax-un 6602 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-reu 2763  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-iun 4271  df-br 4396  df-opab 4455  df-mpt 4456  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-rn 4850  df-res 4851  df-ima 4852  df-iota 5553  df-fun 5591  df-fn 5592  df-f 5593  df-f1 5594  df-fo 5595  df-f1o 5596  df-fv 5597  df-oprab 6312 This theorem is referenced by: (None)
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