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Theorem opeqex 4447
 Description: Equivalence of existence implied by equality of ordered pairs. (Contributed by NM, 28-May-2008.)
Assertion
Ref Expression
opeqex

Proof of Theorem opeqex
StepHypRef Expression
1 neeq1 2609 . 2
2 opnz 4432 . 2
3 opnz 4432 . 2
41, 2, 33bitr3g 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725   wne 2599  cvv 2956  c0 3628  cop 3817 This theorem is referenced by:  oteqex2  4448  oteqex  4449  epelg  4495 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823
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