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Theorem f1orel 5338
Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003.)
Assertion
Ref Expression
f1orel (𝐹:𝐴1-1-onto𝐵 → Rel 𝐹)

Proof of Theorem f1orel
StepHypRef Expression
1 f1ofun 5337 . 2 (𝐹:𝐴1-1-onto𝐵 → Fun 𝐹)
2 funrel 5110 . 2 (Fun 𝐹 → Rel 𝐹)
31, 2syl 14 1 (𝐹:𝐴1-1-onto𝐵 → Rel 𝐹)
Colors of variables: wff set class
Syntax hints:  wi 4  Rel wrel 4514  Fun wfun 5087  1-1-ontowf1o 5092
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-fun 5095  df-fn 5096  df-f 5097  df-f1 5098  df-f1o 5100
This theorem is referenced by:  f1ococnv1  5364  isores1  5683  ssenen  6713  dif1en  6741
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