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Theorem dmopab3 5053
 Description: The domain of a restricted class of ordered pairs. (Contributed by NM, 31-Jan-2004.)
Assertion
Ref Expression
dmopab3
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem dmopab3
StepHypRef Expression
1 df-ral 2761 . 2
2 pm4.71 642 . . 3
32albii 1699 . 2
4 dmopab 5051 . . . . 5
5 19.42v 1842 . . . . . 6
65abbii 2587 . . . . 5
74, 6eqtri 2493 . . . 4
87eqeq1i 2476 . . 3
9 eqcom 2478 . . 3
10 abeq2 2580 . . 3
118, 9, 103bitr2ri 282 . 2
121, 3, 113bitri 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  wex 1671   wcel 1904  cab 2457  wral 2756  copab 4453   cdm 4839 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-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 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-rab 2765  df-v 3033  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-br 4396  df-opab 4455  df-dm 4849 This theorem is referenced by:  dmxp  5059  fnopabg  5711  opabn1stprc  39153
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