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Theorem f1orel 5157
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 5156 . 2 (𝐹:𝐴1-1-onto𝐵 → Fun 𝐹)
2 funrel 4947 . 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 4378  Fun wfun 4924  1-1-ontowf1o 4929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103
This theorem depends on definitions:  df-bi 114  df-fun 4932  df-fn 4933  df-f 4934  df-f1 4935  df-f1o 4937
This theorem is referenced by:  f1ococnv1  5183  isores1  5482  dif1en  6368
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