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Theorem f1rel 5456
Description: A one-to-one onto mapping is a relation. (Contributed by NM, 8-Mar-2014.)
Assertion
Ref Expression
f1rel  |-  ( F : A -1-1-> B  ->  Rel  F )

Proof of Theorem f1rel
StepHypRef Expression
1 f1fn 5454 . 2  |-  ( F : A -1-1-> B  ->  F  Fn  A )
2 fnrel 5358 . 2  |-  ( F  Fn  A  ->  Rel  F )
31, 2syl 15 1  |-  ( F : A -1-1-> B  ->  Rel  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Rel wrel 4710    Fn wfn 5266   -1-1->wf1 5268
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-fun 5273  df-fn 5274  df-f 5275  df-f1 5276
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