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Theorem opswap 5358
 Description: Swap the members of an ordered pair. (Contributed by NM, 14-Dec-2008.) (Revised by Mario Carneiro, 30-Aug-2015.)
Assertion
Ref Expression
opswap

Proof of Theorem opswap
StepHypRef Expression
1 cnvsng 5357 . . . 4
21unieqd 4028 . . 3
3 opex 4429 . . . 4
43unisn 4033 . . 3
52, 4syl6eq 2486 . 2
6 uni0 4044 . . 3
7 opprc 4007 . . . . . . 7
87sneqd 3829 . . . . . 6
98cnveqd 5050 . . . . 5
10 cnvsn0 5340 . . . . 5
119, 10syl6eq 2486 . . . 4
1211unieqd 4028 . . 3
13 ancom 439 . . . 4
14 opprc 4007 . . . 4
1513, 14sylnbi 299 . . 3
166, 12, 153eqtr4a 2496 . 2
175, 16pm2.61i 159 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360   wceq 1653   wcel 1726  cvv 2958  c0 3630  csn 3816  cop 3819  cuni 4017  ccnv 4879 This theorem is referenced by:  2nd1st  6394  cnvf1olem  6446  brtpos  6490  dftpos4  6500  tpostpos  6501  xpcomco  7200  fsumcnv  12559  gsumcom2  15551  txswaphmeolem  17838  fprodcnv  25309 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-xp 4886  df-rel 4887  df-cnv 4888  df-dm 4890  df-rn 4891
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