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Theorem ensn1g 7600
Description: A singleton is equinumerous to ordinal one. (Contributed by NM, 23-Apr-2004.)
Assertion
Ref Expression
ensn1g

Proof of Theorem ensn1g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 4039 . . 3
21breq1d 4462 . 2
3 vex 3112 . . 3
43ensn1 7599 . 2
52, 4vtoclg 3167 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  {csn 4029   class class class wbr 4452   c1o 7142   cen 7533
This theorem is referenced by:  enpr1g  7601  en1b  7603  en2sn  7615  snfi  7616  snnen2o  7726  sucxpdom  7749  en1eqsn  7769  en1eqsnbi  7770  pr2nelem  8403  prdom2  8405  cda1en  8576  rngoueqz  25432  snct  27534
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-suc 4889  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-1o 7149  df-en 7537
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