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Theorem opeqpr 4750
 Description: Equivalence for an ordered pair equal to an unordered pair. (Contributed by NM, 3-Jun-2008.) (Avoid depending on this detail.)
Hypotheses
Ref Expression
opeqpr.1
opeqpr.2
opeqpr.3
opeqpr.4
Assertion
Ref Expression
opeqpr

Proof of Theorem opeqpr
StepHypRef Expression
1 eqcom 2476 . 2
2 opeqpr.1 . . . 4
3 opeqpr.2 . . . 4
42, 3dfop 4218 . . 3
54eqeq2i 2485 . 2
6 opeqpr.3 . . 3
7 opeqpr.4 . . 3
8 snex 4694 . . 3
9 prex 4695 . . 3
106, 7, 8, 9preq12b 4208 . 2
111, 5, 103bitri 271 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wo 368   wa 369   wceq 1379   wcel 1767  cvv 3118  csn 4033  cpr 4035  cop 4039 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040 This theorem is referenced by:  relop  5159
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