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Theorem djulf1or 7048
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 4127 . 2  |-  (/)  e.  _V
2 df-inl 7039 . 2  |- inl  =  ( x  e.  _V  |->  <. (/)
,  x >. )
31, 2djuf1olemr 7046 1  |-  (inl  |`  A ) : A -1-1-onto-> ( { (/) }  X.  A )
Colors of variables: wff set class
Syntax hints:   (/)c0 3422   {csn 3591    X. cxp 4620    |` cres 4624   -1-1-onto->wf1o 5210  inlcinl 7037
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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-sep 4118  ax-nul 4126  ax-pow 4171  ax-pr 4205  ax-un 4429
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-v 2739  df-sbc 2963  df-dif 3131  df-un 3133  df-in 3135  df-ss 3142  df-nul 3423  df-pw 3576  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-opab 4062  df-mpt 4063  df-id 4289  df-xp 4628  df-rel 4629  df-cnv 4630  df-co 4631  df-dm 4632  df-rn 4633  df-res 4634  df-iota 5173  df-fun 5213  df-fn 5214  df-f 5215  df-f1 5216  df-fo 5217  df-f1o 5218  df-fv 5219  df-1st 6134  df-2nd 6135  df-inl 7039
This theorem is referenced by:  inlresf1  7053  djuinr  7055  djuunr  7058  eldju  7060  eninl  7089
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