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Theorem enref 7442
Description: Equinumerosity is reflexive. Theorem 1 of [Suppes] p. 92. (Contributed by NM, 25-Sep-2004.)
Hypothesis
Ref Expression
enref.1  |-  A  e. 
_V
Assertion
Ref Expression
enref  |-  A  ~~  A

Proof of Theorem enref
StepHypRef Expression
1 enref.1 . 2  |-  A  e. 
_V
2 enrefg 7441 . 2  |-  ( A  e.  _V  ->  A  ~~  A )
31, 2ax-mp 5 1  |-  A  ~~  A
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1758   _Vcvv 3068   class class class wbr 4390    ~~ cen 7407
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4511  ax-nul 4519  ax-pow 4568  ax-pr 4629  ax-un 6472
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2264  df-mo 2265  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3070  df-dif 3429  df-un 3431  df-in 3433  df-ss 3440  df-nul 3736  df-if 3890  df-pw 3960  df-sn 3976  df-pr 3978  df-op 3982  df-uni 4190  df-br 4391  df-opab 4449  df-id 4734  df-xp 4944  df-rel 4945  df-cnv 4946  df-co 4947  df-dm 4948  df-rn 4949  df-res 4950  df-ima 4951  df-fun 5518  df-fn 5519  df-f 5520  df-f1 5521  df-fo 5522  df-f1o 5523  df-en 7411
This theorem is referenced by:  ener  7456  en0  7472  pwen  7584  phplem2  7591  phplem3  7592  isinf  7627  pssnn  7632  karden  8203  mappwen  8383  cdacomen  8451  infmap2  8488  ackbij1lem5  8494  axcc4dom  8711  domtriomlem  8712  cfpwsdom  8849  0tsk  9023  fzennn  11891  qnnen  13598  rpnnen  13611  rexpen  13612  lmisfree  18380  met2ndci  20213  lgseisenlem2  22805
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