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Theorem exsnrex 3441
 Description: There is a set being the element of a singleton if and only if there is an element of the singleton. (Contributed by Alexander van der Vekens, 1-Jan-2018.)
Assertion
Ref Expression
exsnrex

Proof of Theorem exsnrex
StepHypRef Expression
1 vex 2577 . . . . . 6
21snid 3430 . . . . 5
3 eleq2 2117 . . . . 5
42, 3mpbiri 161 . . . 4
54pm4.71ri 378 . . 3
65exbii 1512 . 2
7 df-rex 2329 . 2
86, 7bitr4i 180 1
 Colors of variables: wff set class Syntax hints:   wa 101   wb 102   wceq 1259  wex 1397   wcel 1409  wrex 2324  csn 3403 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-sn 3409 This theorem is referenced by: (None)
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