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Theorem opthpr 3968
 Description: A way to represent ordered pairs using unordered pairs with distinct members. (Contributed by NM, 27-Mar-2007.)
Hypotheses
Ref Expression
preq12b.1
preq12b.2
preq12b.3
preq12b.4
Assertion
Ref Expression
opthpr

Proof of Theorem opthpr
StepHypRef Expression
1 preq12b.1 . . 3
2 preq12b.2 . . 3
3 preq12b.3 . . 3
4 preq12b.4 . . 3
51, 2, 3, 4preq12b 3966 . 2
6 idd 22 . . . 4
7 df-ne 2600 . . . . . 6
8 pm2.21 102 . . . . . 6
97, 8sylbi 188 . . . . 5
109imp3a 421 . . . 4
116, 10jaod 370 . . 3
12 orc 375 . . 3
1311, 12impbid1 195 . 2
145, 13syl5bb 249 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359   wceq 1652   wcel 1725   wne 2598  cvv 2948  cpr 3807 This theorem is referenced by:  brdom7disj  8401  brdom6disj  8402 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-un 3317  df-sn 3812  df-pr 3813
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