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Theorem copsex4g 4690
 Description: An implicit substitution inference for 2 ordered pairs. (Contributed by NM, 5-Aug-1995.)
Hypothesis
Ref Expression
copsex4g.1
Assertion
Ref Expression
copsex4g
Distinct variable groups:   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,
Allowed substitution hints:   (,,,)

Proof of Theorem copsex4g
StepHypRef Expression
1 eqcom 2478 . . . . . . 7
2 vex 3034 . . . . . . . 8
3 vex 3034 . . . . . . . 8
42, 3opth 4676 . . . . . . 7
51, 4bitri 257 . . . . . 6
6 eqcom 2478 . . . . . . 7
7 vex 3034 . . . . . . . 8
8 vex 3034 . . . . . . . 8
97, 8opth 4676 . . . . . . 7
106, 9bitri 257 . . . . . 6
115, 10anbi12i 711 . . . . 5
1211anbi1i 709 . . . 4
1312a1i 11 . . 3
14134exbidv 1780 . 2
15 id 22 . . 3
16 copsex4g.1 . . 3
1715, 16cgsex4g 3068 . 2
1814, 17bitrd 261 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376   wceq 1452  wex 1671   wcel 1904  cop 3965 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-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  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 This theorem is referenced by:  opbrop  4919  ov3  6452
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