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Theorem f1orel 5430
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 5429 . 2 (𝐹:𝐴1-1-onto𝐵 → Fun 𝐹)
2 funrel 5200 . 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 4604  Fun wfun 5177  1-1-ontowf1o 5182
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 5185  df-fn 5186  df-f 5187  df-f1 5188  df-f1o 5190
This theorem is referenced by:  f1ococnv1  5456  isores1  5777  ssenen  6809  dif1en  6837
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