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Theorem djulf1or 7086
Description: The left injection function on all sets is one to one and onto. (Contributed by BJ and Jim Kingdon, 22-Jun-2022.)
Assertion
Ref Expression
djulf1or  |-  (inl  |`  A ) : A -1-1-onto-> ( { (/) }  X.  A )

Proof of Theorem djulf1or
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 0ex 4145 . 2  |-  (/)  e.  _V
2 df-inl 7077 . 2  |- inl  =  ( x  e.  _V  |->  <. (/)
,  x >. )
31, 2djuf1olemr 7084 1  |-  (inl  |`  A ) : A -1-1-onto-> ( { (/) }  X.  A )
Colors of variables: wff set class
Syntax hints:   (/)c0 3437   {csn 3607    X. cxp 4642    |` cres 4646   -1-1-onto->wf1o 5234  inlcinl 7075
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-nul 4144  ax-pow 4192  ax-pr 4227  ax-un 4451
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-sbc 2978  df-dif 3146  df-un 3148  df-in 3150  df-ss 3157  df-nul 3438  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-opab 4080  df-mpt 4081  df-id 4311  df-xp 4650  df-rel 4651  df-cnv 4652  df-co 4653  df-dm 4654  df-rn 4655  df-res 4656  df-iota 5196  df-fun 5237  df-fn 5238  df-f 5239  df-f1 5240  df-fo 5241  df-f1o 5242  df-fv 5243  df-1st 6166  df-2nd 6167  df-inl 7077
This theorem is referenced by:  inlresf1  7091  djuinr  7093  djuunr  7096  eldju  7098  eninl  7127
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