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Theorem snel1cg 4141
 Description: A singleton is an element of cardinal one. (Contributed by SF, 30-Jan-2015.)
Assertion
Ref Expression
snel1cg 1c

Proof of Theorem snel1cg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 3744 . . 3
21eleq1d 2419 . 2 1c 1c
3 vex 2862 . . 3
43snel1c 4140 . 2 1c
52, 4vtoclg 2914 1 1c
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  csn 3737  1cc1c 4134 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-1c 4136 This theorem is referenced by:  snfi  4431  ncfinsn  4476  nchoicelem13  6301
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