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Theorem enref 6894
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 6893 . 2  |-  ( A  e.  _V  ->  A  ~~  A )
31, 2ax-mp 8 1  |-  A  ~~  A
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   _Vcvv 2788   class class class wbr 4023    ~~ cen 6860
This theorem is referenced by:  ener  6908  en0  6924  pwen  7034  phplem2  7041  phplem3  7042  isinf  7076  pssnn  7081  karden  7565  mappwen  7739  cdacomen  7807  infmap2  7844  ackbij1lem5  7850  axcc4dom  8067  domtriomlem  8068  cfpwsdom  8206  0tsk  8377  fzennn  11030  qnnen  12492  rpnnen  12505  rexpen  12506  met2ndci  18068  lgseisenlem2  20589  lmisfree  27312
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-pw 3627  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-fun 5257  df-fn 5258  df-f 5259  df-f1 5260  df-fo 5261  df-f1o 5262  df-en 6864
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