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Theorem prex 4112
 Description: An unordered pair exists. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
prex {A, B} V

Proof of Theorem prex
StepHypRef Expression
1 df-pr 3742 . 2 {A, B} = ({A} ∪ {B})
2 snex 4111 . . 3 {A} V
3 snex 4111 . . 3 {B} V
42, 3unex 4106 . 2 ({A} ∪ {B}) V
51, 4eqeltri 2423 1 {A, B} V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  Vcvv 2859   ∪ cun 3207  {csn 3737  {cpr 3738 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742 This theorem is referenced by:  opkex  4113  elopk  4129  opkthg  4131  enprmaplem5  6080  2p1e3c  6156  ce2  6192
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