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Theorem enpr1g 7173
Description:  { A ,  A } has only one element. (Contributed by FL, 15-Feb-2010.)
Assertion
Ref Expression
enpr1g  |-  ( A  e.  V  ->  { A ,  A }  ~~  1o )

Proof of Theorem enpr1g
StepHypRef Expression
1 dfsn2 3828 . 2  |-  { A }  =  { A ,  A }
2 ensn1g 7172 . 2  |-  ( A  e.  V  ->  { A }  ~~  1o )
31, 2syl5eqbrr 4246 1  |-  ( A  e.  V  ->  { A ,  A }  ~~  1o )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   {csn 3814   {cpr 3815   class class class wbr 4212   1oc1o 6717    ~~ cen 7106
This theorem is referenced by:  pr2ne  7889
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-13 1727  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  ax-un 4701
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-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  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  df-uni 4016  df-br 4213  df-opab 4267  df-id 4498  df-suc 4587  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-1o 6724  df-en 7110
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