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Theorem f1orel 5755
Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003.)
Assertion
Ref Expression
f1orel  |-  ( F : A -1-1-onto-> B  ->  Rel  F )

Proof of Theorem f1orel
StepHypRef Expression
1 f1ofun 5754 . 2  |-  ( F : A -1-1-onto-> B  ->  Fun  F )
2 funrel 5546 . 2  |-  ( Fun 
F  ->  Rel  F )
31, 2syl 16 1  |-  ( F : A -1-1-onto-> B  ->  Rel  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Rel wrel 4956   Fun wfun 5523   -1-1-onto->wf1o 5528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-fun 5531  df-fn 5532  df-f 5533  df-f1 5534  df-f1o 5536
This theorem is referenced by:  f1ococnv1  5780  isores1  6137  weisoeq2  6159  f1oexrnex  6640  ssenen  7598  cantnffval2  8017  cantnffval2OLD  8039  hasheqf1oi  12242  cmphaushmeo  19508  f1ocan2fv  28789  ltrncnvnid  34129
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